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Автор: Grafiati

Опубліковано: 6 вересня 2023

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1

Muller, M. A. "Bornologiese pseudotopologiese vektorruimtes." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 9, no. 1 (July 5, 1990): 15–18. http://dx.doi.org/10.4102/satnt.v9i1.434.

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Homological spaces were defined by Hogbe-Nlend in 1971 and pseudo-topological spaces by Fischer in 1959. In this paper properties of bornological pseudo-topological vector spaces are investigated. A characterization of such spaces is obtained and it is shown that quotient spaces and direct sums o f boruological pseudo-topological vector spaces are bornological. Every bornological locally convex pseudo-topological vector space is shown to be the inductive limit in the category of pseudo-topological vector spaces of a family of locally convex topological vector spaces.

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2

Gabriyelyan, Saak S., and Sidney A. Morris. "Free Subspaces of Free Locally Convex Spaces." Journal of Function Spaces 2018 (2018): 1–5. http://dx.doi.org/10.1155/2018/2924863.

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IfXandYare Tychonoff spaces, letL(X)andL(Y)be the free locally convex space overXandY, respectively. For generalXandY, the question of whetherL(X)can be embedded as a topological vector subspace ofL(Y)is difficult. The best results in the literature are that ifL(X)can be embedded as a topological vector subspace ofL(I), whereI=[0,1], thenXis a countable-dimensional compact metrizable space. Further, ifXis a finite-dimensional compact metrizable space, thenL(X)can be embedded as a topological vector subspace ofL(I). In this paper, it is proved thatL(X)can be embedded inL(R)as a topological vector subspace ifXis a disjoint union of a countable number of finite-dimensional locally compact separable metrizable spaces. This is the case ifX=Rn, n∈N.It is also shown that ifGandQdenote the Cantor space and the Hilbert cubeIN, respectively, then (i)L(X)is embedded inL(G)if and only ifXis a zero-dimensional metrizable compact space; (ii)L(X)is embedded inL(Q)if and only ifYis a metrizable compact space.

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3

Park, Sehie. "Best approximation theorems for composites of upper semicontinuous maps." Bulletin of the Australian Mathematical Society 51, no. 2 (April 1995): 263–72. http://dx.doi.org/10.1017/s000497270001409x.

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Let (E, τ) be a Hausdorff topological vector space and (X, ω) a weakly compact convex subset of E with the relative weak topology ω. Recently, there have appeared best approximation and fixed point theorems for convex-valued upper semicontinuous maps F: (X, ω) → 2(E, τ) whenever (E, τ) is locally convex. In this paper, these results are extended to a very broad class of multifunctions containing composites of acyclic maps in a topological vector space having sufficiently many linear functionals. Moreover, we also obtain best approximation theorems for classes of multifunctions defined on approximatively compact convex subsets of locally convex Hausdorff topological vector spaces or closed convex subsets of Banach spaces with the Oshman property.

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4

Robertson, W. J., S. A. Saxon, and A. P. Robertson. "Barrelled spaces and dense vector subspaces." Bulletin of the Australian Mathematical Society 37, no. 3 (June 1988): 383–88. http://dx.doi.org/10.1017/s0004972700027003.

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This note presents a structure theorem for locally convex barrelled spaces. It is shown that, corresponding to any Hamel basis, there is a natural splitting of a barrelled space into a topological sum of two vector subspaces, one with its strongest locally convex topology. This yields a simple proof that a barrelled space has a dense infinite-codimensional vector subspace, provided that it does not have its strongest locally convex topology. Some further results and examples discuss the size of the codimension of a dense vector subspace.

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5

DE BEER, RICHARD J. "TAUBERIAN THEOREMS AND SPECTRAL THEORY IN TOPOLOGICAL VECTOR SPACES." Glasgow Mathematical Journal 55, no. 3 (February 25, 2013): 511–32. http://dx.doi.org/10.1017/s0017089512000699.

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AbstractWe investigate the spectral theory of integrable actions of a locally compact abelian group on a locally convex vector space. We start with an analysis of various spectral subspaces induced by the action of the group. This is applied to analyse the spectral theory of operators on the space, generated by measures on the group. We apply these results to derive general Tauberian theorems that apply to arbitrary locally compact abelian groups acting on a large class of locally convex vector spaces, which includes Fréchet spaces. We show how these theorems simplify the derivation of Mean Ergodic theorems.

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6

Robertson, Neill. "Extending Edgar's ordering to locally convex spaces." Glasgow Mathematical Journal 34, no. 2 (May 1992): 175–88. http://dx.doi.org/10.1017/s0017089500008697.

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By the term “locally convex space”, we mean a locally convex Hausdorff topological vector space (see [17]). We shall denote the algebraic dual of a locally convex space E by E*, and its topological dual by E′. It is convenient to think of the elements of E as being linear functionals on E′, so that E can be identified with a subspace of E′*. The adjoint of a continuous linear map T:E→F will be denoted by T′:F′→E′. If 〈E, F〈 is a dual pair of vector spaces, then we shall denote the corresponding weak, strong and Mackey topologies on E by α(E, F), β(E, F) and μ(E, F) respectively.

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7

Glöckner, Helge. "Aspects of Differential Calculus Related to Infinite-Dimensional Vector Bundles and Poisson Vector Spaces." Axioms 11, no. 5 (May 9, 2022): 221. http://dx.doi.org/10.3390/axioms11050221.

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We prove various results in infinite-dimensional differential calculus that relate the differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: (1) in the theory of infinite-dimensional vector bundles, to construct new bundles from given ones, such as dual bundles, topological tensor products, infinite direct sums, and completions (under suitable hypotheses); (2) in the theory of locally convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity of passage from a function to the associated Hamiltonian vector field. Topological properties of topological vector spaces are essential for the studies, which allow the hypocontinuity of bilinear mappings to be exploited. Notably, we encounter kR-spaces and locally convex spaces E such that E×E is a kR-space.

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8

Khan, Liaqat Ali, and Saud M. Alsulami. "Asymptotic Almost Periodic Functions with Range in a Topological Vector Space." Journal of Function Spaces and Applications 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/965746.

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The notion of asymptotic almost periodicity was first introduced by Fréchet in 1941 in the case of finite dimensional range spaces. Later, its extension to the case of Banach range spaces and locally convex range spaces has been considered by several authors. In this paper, we have generalized the concept of asymptotic almost periodicity to the case where the range space is a general topological vector space, not necessarily locally convex. Our results thus widen the scope of applications of asymptotic almost periodicity.

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9

García-Pacheco, Francisco Javier, Soledad Moreno-Pulido, Enrique Naranjo-Guerra, and Alberto Sánchez-Alzola. "Non-Linear Inner Structure of Topological Vector Spaces." Mathematics 9, no. 5 (February 25, 2021): 466. http://dx.doi.org/10.3390/math9050466.

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Inner structure appeared in the literature of topological vector spaces as a tool to characterize the extremal structure of convex sets. For instance, in recent years, inner structure has been used to provide a solution to The Faceless Problem and to characterize the finest locally convex vector topology on a real vector space. This manuscript goes one step further by settling the bases for studying the inner structure of non-convex sets. In first place, we observe that the well behaviour of the extremal structure of convex sets with respect to the inner structure does not transport to non-convex sets in the following sense: it has been already proved that if a face of a convex set intersects the inner points, then the face is the whole convex set; however, in the non-convex setting, we find an example of a non-convex set with a proper extremal subset that intersects the inner points. On the opposite, we prove that if a extremal subset of a non-necessarily convex set intersects the affine internal points, then the extremal subset coincides with the whole set. On the other hand, it was proved in the inner structure literature that isomorphisms of vector spaces and translations preserve the sets of inner points and outer points. In this manuscript, we show that in general, affine maps and convex maps do not preserve inner points. Finally, by making use of the inner structure, we find a simple proof of the fact that a convex and absorbing set is a neighborhood of 0 in the finest locally convex vector topology. In fact, we show that in a convex set with internal points, the subset of its inner points coincides with the subset of its internal points, which also coincides with its interior with respect to the finest locally convex vector topology.

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10

Maza, Rodolfo Erodias, and Sergio Rosales Canoy, Jr. "Denjoy-type Integrals in Locally Convex Topological Vector Space." European Journal of Pure and Applied Mathematics 14, no. 4 (November 10, 2021): 1169–83. http://dx.doi.org/10.29020/nybg.ejpam.v14i4.4115.

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Анотація:

In this paper, we introduce AC* and ACG*-type properties and then, using theseconditions along with other concepts, define two Denjoy-type integrals of a function with values in a locally convex topological vector space (LCTVS). We show, among others, that these newly defined integrals are included in the SH integral, a stronger version of the Henstock integral for LCTVS-valued functions.

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11

Giannakoulias, Efstathios. "Some properties of vector measures taking values in a topological vector space." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 43, no. 2 (October 1987): 224–30. http://dx.doi.org/10.1017/s1446788700029360.

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AbstractIn this paper we study some properties of vector measures with values in various topological vector spaces. As a matter of fact, we give a necessary condition implying the Pettis integrability of a function f: S → E, where S is a set and E a locally convex space. Furthermore, we prove an iff condition under which (Q, E) has the Pettis property, for an algebra Q and a sequentially complete topological vector space E. An approximating theorem concerning vector measures taking values in a Fréchet space is also given.

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12

Zhang, Hui, and Jin-xuan Fang. "On locally convex I-topological vector spaces." Fuzzy Sets and Systems 157, no. 14 (July 2006): 1995–2002. http://dx.doi.org/10.1016/j.fss.2006.02.006.

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13

ARIYAWANSA, K. A., W. C. DAVIDON, and K. D. McKENNON. "A CHARACTERIZATION OF CONVEXITY-PRESERVING MAPS FROM A SUBSET OF A VECTOR SPACE INTO ANOTHER VECTOR SPACE." Journal of the London Mathematical Society 64, no. 1 (August 2001): 179–90. http://dx.doi.org/10.1017/s0024610701002204.

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Анотація:

Let V and X be Hausdorff, locally convex, real, topological vector spaces with dim V > 1. It is shown that a map σ from an open, connected subset of V onto an open subset of X is homeomorphic and convexity-preserving if and only if σ is projective.

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14

Saveliev, Peter. "Fixed points and selections of set-valued maps on spaces with convexity." International Journal of Mathematics and Mathematical Sciences 24, no. 9 (2000): 595–612. http://dx.doi.org/10.1155/s0161171200004403.

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We provide theorems extending both Kakutani and Browder fixed points theorems for multivalued maps on topological vector spaces, as well as some selection theorems. For this purpose we introduce convex structures more general than those of locally convex and non-locally convex topological vector spaces or generalized convexity structures due to Michael, van de Vel, and Horvath.

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15

Khan, L. A., and A. B. Thaheem. "Multiplication operators on weighted spaces in the non-locally convex framework." International Journal of Mathematics and Mathematical Sciences 20, no. 1 (1997): 75–79. http://dx.doi.org/10.1155/s0161171297000112.

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LetXbe a completely regular Hausdorff space,Ea topological vector space,Va Nachbin family of weights onX, andCV0(X,E)the weighted space of continuousE-valued functions onX. Letθ:X→Cbe a mapping,f∈CV0(X,E)and defineMθ(f)=θf(pointwise). In caseEis a topological algebra,ψ:X→Eis a mapping then defineMψ(f)=ψf(pointwise). The main purpose of this paper is to give necessary and sufficient conditions forMθandMψto be the multiplication operators onCV0(X,E)whereEis a general topological space (or a suitable topological algebra) which is not necessarily locally convex. These results generalize recent work of Singh and Manhas based on the assumption thatEis locally convex.

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16

DAS, Abhishikta, and Tarapada BAG. "A Note on Equivalence of G-Cone Metric Spaces and G-Metric Spaces." Journal of New Theory, no. 43 (June 30, 2023): 73–82. http://dx.doi.org/10.53570/jnt.1277026.

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This paper contains the equivalence between tvs-G cone metric and G-metric using a scalarization function $\zeta_p$, defined over a locally convex Hausdorff topological vector space. This function ensures that most studies on the existence and uniqueness of fixed-point theorems on G-metric space and tvs-G cone metric spaces are equivalent. We prove the equivalence between the vector-valued version and scalar-valued version of the fixed-point theorems of those spaces. Moreover, we present that if a real Banach space is considered instead of a locally convex Hausdorff space, then the theorems of this article extend some results of G-cone metric spaces and ensure the correspondence between any G-cone metric space and the G-metric space.

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17

Zabeti, Omid, and Ljubisa Kocinac. "A few remarks on bounded operators on topological vector spaces." Filomat 30, no. 3 (2016): 763–72. http://dx.doi.org/10.2298/fil1603763z.

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Анотація:

We give a few observations on different types of bounded operators on a topological vector space X and their relations with compact operators on X. In particular, we investigate when these bounded operators coincide with compact operators. We also consider similar types of bounded bilinear mappings between topological vector spaces. Some properties of tensor product operators between locally convex spaces are established. In the last part of the paper we deal with operators on topological Riesz spaces.

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18

Reiland, Thomas W. "Nonsmooth analysis and optimization on partially ordered vector spaces." International Journal of Mathematics and Mathematical Sciences 15, no. 1 (1992): 65–81. http://dx.doi.org/10.1155/s0161171292000085.

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Interval-Lipschitz mappings between topological vector spaces are defined and compared with other Lipschitz-type operators. A theory of generalized gradients is presented when both spaces are locally convex and the range space is an order complete vector lattice. Sample applications to the theory of nonsmooth optimization are given.

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19

Singh, R. K., and Jasbir Singh Manhas. "Multiplication Operators and Dynamical Systems." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 53, no. 1 (August 1992): 92–102. http://dx.doi.org/10.1017/s1446788700035424.

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AbstractLet X be a completely regular Hausdorff space, let V be a system of weights on X and let T be a locally convex Hausdorff topological vector space. Then CVb(X, T) is a locally convex space of vector-valued continuous functions with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present paper we characterize multiplication operators on the space CVb(X, T) induced by operator-valued mappings and then obtain a (linear) dynamical system on this weighted function space.

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20

Khurana, Surjit Singh. "Vector Measures on Topological Spaces." gmj 14, no. 4 (December 2007): 687–98. http://dx.doi.org/10.1515/gmj.2007.687.

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Abstract Let 𝑋 be a completely regular Hausdorff space, 𝐸 a quasi-complete locally convex space, 𝐶(𝑋) (resp. 𝐶𝑏(𝑋)) the space of all (resp. all, bounded), scalar-valued continuous functions on 𝑋, and 𝐵(𝑋) and 𝐵0(𝑋) be the classes of Borel and Baire subsets of 𝑋. We study the spaces 𝑀𝑡(𝑋,𝐸), 𝑀 τ (𝑋,𝐸), 𝑀 σ (𝑋,𝐸) of tight, τ-smooth, σ-smooth, 𝐸-valued Borel and Baire measures on 𝑋. Using strict topologies, we prove some measure representation theorems of linear operators between 𝐶𝑏(𝑋) and 𝐸 and then prove some convergence theorems about integrable functions. Also, the Alexandrov's theorem is extended to the vector case and a representation theorem about the order-bounded, scalar-valued, linear maps from 𝐶(𝑋) is generalized to the vector-valued linear maps.

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21

Iro, Ain, and Leiki Loone. "Knopp’s core in topological vector spaces." Acta et Commentationes Universitatis Tartuensis de Mathematica 2 (December 31, 1998): 75–79. http://dx.doi.org/10.12697/acutm.1998.02.11.

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22

BERLANGA, RICARDO. "A TOPOLOGISED MEASURE HOMOLOGY." Glasgow Mathematical Journal 50, no. 3 (September 2008): 359–69. http://dx.doi.org/10.1017/s0017089508004266.

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AbstractA homology theory based on measures, first mentioned by Thurston, is naturally defined here as a functor into the category of locally convex topological vector spaces. It is proved that the first homology space is Hausdorff.

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23

Nguyen, Dinh, and Mo Hong Tran. "Asymptotic Farkas lemmas for convex systems." Science and Technology Development Journal 19, no. 4 (December 31, 2016): 160–68. http://dx.doi.org/10.32508/stdj.v19i4.812.

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Анотація:

In this paper we establish characterizations of the containment of the set {xX: xC,g(x)K}{xX: f (x)0}, where C is a closed convex subset of a locally convex Hausdorff topological vector space, X, K is a closed convex cone in another locally convex Hausdorff topological vector space and g:X Y is a K- convex mapping, in a reverse convex set, define by the proper, lower semicontinuous, convex function. Here, no constraint qualification condition or qualification condition are assumed. The characterizations are often called asymptotic Farkas-type results. The second part of the paper was devoted to variant Asymptotic Farkas-type results where the mapping is a convex mapping with respect to an extended sublinear function. It is also shown that under some closedness conditions, these asymptotic Farkas lemmas go back to non-asymptotic Farkas lemmas or stable Farkas lemmas established recently in the literature. The results can be used to study the optimization

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24

Zheng, X. Y. "Proper Efficiency in Locally Convex Topological Vector Spaces." Journal of Optimization Theory and Applications 94, no. 2 (August 1997): 469–86. http://dx.doi.org/10.1023/a:1022648115446.

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25

Hõim, Terje, and David A. Robbins. "Strict topologies on spaces of vector-valued functions." Acta et Commentationes Universitatis Tartuensis de Mathematica 14 (December 31, 2010): 75–90. http://dx.doi.org/10.12697/acutm.2010.14.08.

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Анотація:

Let X be a completely regular Hausdorff space, and {Ex : x ∈ X} a collection of non-trivial locally convex topological vector spaces indexed by X. Let E be their disjoint union. We investigate a species of strict topology on a vector space F of choice functions σ : X → E (σ(x) ∈ Ex), and obtain Stone–Weierstrass and spectral synthesis analogues. We also obtain completeness results in some special cases.

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26

García-Martínez, Armando. "Webbed spaces, double sequences, and the Macke convergence condition." International Journal of Mathematics and Mathematical Sciences 22, no. 3 (1999): 521–24. http://dx.doi.org/10.1155/s0161171299225215.

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Анотація:

In [3], Gilsdorf proved, for locally convex spaces, that every sequentially webbed space satisfies the Mackey convergence condition. In the more general frame of topological vector spaces, this theorem and its inverse are studied. The techniques used are double sequences and the localization theorem for webbed spaces.

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27

Abdul-Hussein, Mushtaq Shaker, and G. S. Srivastava. "A study on bornological properties of the space of entire functions of several complex variables." Tamkang Journal of Mathematics 33, no. 4 (December 31, 2002): 289–302. http://dx.doi.org/10.5556/j.tkjm.33.2002.277.

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Spaces of entire functions of several complex variables occupy an important position in view of their vast applications in various branches of mathematics, for instance, the classical analysis, theory of approximation, theory of topological bases etc. With an idea of correlating entire functions with certain aspects in the theory of basis in locally convex spaces, we have investigated in this paper the bornological aspects of the space $X$ of integral functions of several complex variables. By $Y$ we denote the space of all power series with positive radius of convergence at the origin. We introduce bornologies on $X$ and $Y$ and prove that $Y$ is a convex bornological vector space which is the completion of the convex bornological vector space $X$.

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28

Hennings, M. A. "A characterisation of C*-algebras." Proceedings of the Edinburgh Mathematical Society 30, no. 3 (October 1987): 445–53. http://dx.doi.org/10.1017/s0013091500026845.

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Анотація:

It is of some interest to the theory of locally convex *-algebras to know under what conditions such an algebra A is a pre-C*-algebra (the topology of A can be described by a submultiplicative norm such that ‖x*x‖ = ‖x‖2, ∀x∈A). We recall that a locally convex *-algebra is a complex *-algebra A with the structure of a Hausdorff locally convex topological vector space such that the multiplication is separately continuous, and the involution is continuous.

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29

Khan, Liaqat Ali. "On approximation in weighted spaces of continuous vector-valued functions." Glasgow Mathematical Journal 29, no. 1 (January 1987): 65–68. http://dx.doi.org/10.1017/s0017089500006662.

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Анотація:

The fundamental work on approximation in weighted spaces of continuous functions on a completely regular space has been done mainly by Nachbin ([5], [6]). Further investigations have been made by Summers [10], Prolla ([7], [8]), and other authors (see the monograph [8] for more references). These authors considered functions with range contained in the scalar field or a locally convex topological vector space. In the present paper we prove some approximation results without local convexity of the range space.

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30

Ansari-Piri, E. "A class of factorable topological algebras." Proceedings of the Edinburgh Mathematical Society 33, no. 1 (February 1990): 53–59. http://dx.doi.org/10.1017/s001309150002887x.

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Анотація:

The famous Cohen factorization theorem, which says that every Banach algebra with bounded approximate identity factors, has already been generalized to locally convex algebras with what may be termed “uniformly bounded approximate identities”. Here we introduce a new notion, that of fundamentality generalizing both local boundedness and local convexity, and we show that a fundamental Fréchet algebra with uniformly bounded approximate identity factors. Fundamentality is a topological vector space property rather than an algebra property. We exhibit some non-fundamental topological vector space and give a necessary condition for Orlicz space to be fundamental.

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31

Ayaseha, Davood. "Finite dimensional locally convex cones." Filomat 31, no. 16 (2017): 5111–16. http://dx.doi.org/10.2298/fil1716111a.

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Анотація:

We study the locally convex cones which have finite dimension. We introduce the Euclidean convex quasiuniform structure on a finite dimensional cone. In special case of finite dimensional locally convex topological vector spaces, the symmetric topology induced by the Euclidean convex quasiuniform structure reduces to the known concept of Euclidean topology. We prove that the dual of a finite dimensional cone endowed with the Euclidean convex quasiuniform structure is identical with it?s algebraic dual.

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32

ANTOINE, J. P., F. BAGARELLO, and C. TRAPANI. "TOPOLOGICAL PARTIAL *-ALGEBRAS: BASIC PROPERTIES AND EXAMPLES." Reviews in Mathematical Physics 11, no. 03 (March 1999): 267–302. http://dx.doi.org/10.1142/s0129055x99000106.

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Анотація:

Let [Formula: see text] be a partial *-algebra endowed with a topology τ that makes it into a locally convex topological vector space [Formula: see text]. Then [Formula: see text] is called a topological partial *-algebra if it satisfies a number of conditions, which all amount to require that the topology τ fits with the multiplier structure of [Formula: see text]. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of potential topological partial *-algebras, either function spaces (lattices of Lp spaces on [0, 1] or on ℝ, amalgam spaces), or partial *-algebras of operators (operators on a partial inner product space, O*-algebras).

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33

Hadžić, Olga. "A coincidence theorem in topological vector spaces." Bulletin of the Australian Mathematical Society 33, no. 3 (June 1986): 373–82. http://dx.doi.org/10.1017/s0004972700003956.

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Анотація:

In this paper we prove a coincidence theorem in not necessarily locally convex topological vector spaces, which contains, as a special case, a coincidence theorem proved by Felix Browder. As an application, a result about the existence of maximal elements is obtained.

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34

Daraby, B., N. Khosravi, and A. Rahimi. "Fuzzy barrels on locally convex fuzzy topological vector spaces." Miskolc Mathematical Notes 21, no. 2 (2020): 781. http://dx.doi.org/10.18514/mmn.2020.3197.

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35

Alpay, Daniel, Olga Timoshenko, and Dan Volok. "Carathéodory–Fejér interpolation in locally convex topological vector spaces." Linear Algebra and its Applications 431, no. 8 (September 2009): 1257–66. http://dx.doi.org/10.1016/j.laa.2009.04.023.

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36

Zhang, Hua-Peng, and Jin-Xuan Fang. "New definition of locally convex L-topological vector spaces." Fuzzy Sets and Systems 160, no. 9 (May 2009): 1245–55. http://dx.doi.org/10.1016/j.fss.2008.09.003.

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37

Kakol, Jerzy. "Basic sequences and non locally convex topological vector spaces." Rendiconti del Circolo Matematico di Palermo 36, no. 1 (February 1987): 95–102. http://dx.doi.org/10.1007/bf02844702.

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38

Verma, Ram U. "Variational inequalities in locally convex Hausdorff topological vector spaces." Archiv der Mathematik 71, no. 3 (September 1, 1998): 246–48. http://dx.doi.org/10.1007/s000130050260.

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39

Nowak, Marian. "Topological Properties of the Complex Vector Lattice of Bounded Measurable Functions." Journal of Function Spaces and Applications 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/343685.

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Анотація:

Let Σ be aσ-algebra of subsets of a nonempty set Ω. Let be the complex vector lattice of bounded Σ-measurable complex-valued functions on Ω and let be the Banach space of all bounded countably additive complex-valued measures on Ω. We study locally solid topologies on . In particular, it is shown that the Mackey topology is the finest locally convex-solidσ-Lebesgue topology on .

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40

Pahari, NP. "On Locally Convex Topological Vector Space Valued Paranormed Function Space Defined by Orlicz Function." Nepal Journal of Science and Technology 14, no. 2 (May 15, 2014): 109–16. http://dx.doi.org/10.3126/njst.v14i2.10423.

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Анотація:

The aim of this paper is to introduce and study a new class (l∞ (X, Y, Φ, ξ, w , L), HU) of locally convex space Y- valued functions using Orlicz function Φ as a generalization of some of the well known sequence spaces and function spaces. Besides the investigation pertaining to the linear topological structures of the class (l∞ (X, Y, Φ, ξ, w , L), HU) when topologized it with suitable natural paranorm , our primarily interest is to explore the conditions pertaining the containment relation of the class l∞ (X, Y, Φ, ξ, w) in terms of different ξ and w so that such a class of functions is contained in or equal to another class of similar nature. DOI: http://dx.doi.org/10.3126/njst.v14i2.10423 Nepal Journal of Science and Technology Vol. 14, No. 2 (2013) 109-116

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41

Gupta, Manjul, and Kalika Kaushal. "Topological properties and matrix transformations of certain ordered generalized sequence spaces." International Journal of Mathematics and Mathematical Sciences 18, no. 2 (1995): 341–56. http://dx.doi.org/10.1155/s0161171295000433.

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Анотація:

In this note, we carry out investigations related to the mixed impact of ordering and topological structure of a locally convex solid Riesz space(X,τ)and a scalar valued sequence spaceλ, on the vector valued sequence spaceλ(X)which is formed and topologized with the help ofλandX, and vice versa. Besides,we also characterizeo-matrix transformations fromc(X),ℓ∞(X)to themselves,cs(X)toc(X)and derive necessary conditions for a matrix of linear operators to transformℓ1(X)into a simple ordered vector valued sequence spaceΛ(X).

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42

Ding, Xie Ping, and Kok-Keong Tan. "A Set-Valued Generalization of Fan's Best Approximation Theorem." Canadian Journal of Mathematics 44, no. 4 (August 1, 1992): 784–96. http://dx.doi.org/10.4153/cjm-1992-046-9.

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Анотація:

AbstractLet (E, T) be a Hausdorff topological vector space whose topological dual separates points of E, X be a non-empty weakly compact convex subset of E and W be the relative weak topology on X. If F: (X, W) → 2(E,T) is continuous (respectively, upper semi-continuous if £ is locally convex), approximation and fixed point theorems are obtained which generalize the corresponding results of Fan, Park, Reich and Sehgal-Singh-Smithson (respectively, Ha, Reich, Park, Browder and Fan) in several aspects.

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43

García-Pacheco, Francisco Javier, and Enrique Naranjo-Guerra. "Inner structure in real vector spaces." Georgian Mathematical Journal 27, no. 3 (September 1, 2020): 361–66. http://dx.doi.org/10.1515/gmj-2018-0048.

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Анотація:

AbstractInternal points were introduced in the literature of topological vector spaces to characterize the finest locally convex vector topology. In this manuscript we generalize the concept of internal point in real vector spaces by introducing a type of points, called inner points, that allows us to provide an intrinsic characterization of linear manifolds, which was not possible by using internal points. We also characterize infinite dimensional real vector spaces by means of the inner points of convex sets. Finally, we prove that in convex sets containing internal points, the set of inner points coincides with the one of internal points.

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44

Tang, Yanxia, Jinyu Guan, Pengcheng Ma, Yongchun Xu, and Yongfu Su. "Generalized contraction mapping principle in locally convex topological vector spaces." Journal of Nonlinear Sciences and Applications 09, no. 06 (June 25, 2016): 4659–65. http://dx.doi.org/10.22436/jnsa.009.06.105.

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45

Haluška. "ABOUT A WEAK INTEGRAL IN LOCALLY CONVEX TOPOLOGICAL VECTOR SPACES." Real Analysis Exchange 25, no. 1 (1999): 139. http://dx.doi.org/10.2307/44153056.

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46

Shih, Mau-Hsiang, and Kok-Keong Tan. "Generalized quasi-variational inequalities in locally convex topological vector spaces." Journal of Mathematical Analysis and Applications 108, no. 2 (June 1985): 333–43. http://dx.doi.org/10.1016/0022-247x(85)90029-0.

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47

Bonales, Fernando Garibay, and Rigoberto Vera Mendoza. "A formula to calculate the spectral radius of a compact linear operator." International Journal of Mathematics and Mathematical Sciences 20, no. 3 (1997): 585–88. http://dx.doi.org/10.1155/s0161171297000793.

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Анотація:

There is a formula (Gelfand's formula) to find the spectral radius of a linear operator defined on a Banach space. That formula does not apply even in normed spaces which are not complete. In this paper we show a formula to find the spectral radius of any linear and compact operatorTdefined on a complete topological vector space, locally convex. We also show an easy way to find a non-trivialT-invariant closed subspace in terms of Minkowski functional.

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48

Voisei, M. D. "The Minimal Context for Local Boundedness in Topological Vector Spaces." Annals of the Alexandru Ioan Cuza University - Mathematics 59, no. 2 (July 1, 2013): 219–35. http://dx.doi.org/10.2478/v10157-012-0041-8.

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Анотація:

Abstract The local boundedness of classes of operators is analyzed on different subsets directly related to the Fitzpatrick function associated to an operator. Characterizations of the topological vector spaces for which that local boundedness holds is given in terms of the uniform boundedness principle. For example the local boundedness of a maximal monotone operator on the algebraic interior of its domain convex hull is a characteristic of barreled locally convex spaces.

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49

Bernal, Antonio, and Joan Cerdà. "Analyticity and quasi-Banach valued functions." Bulletin of the Australian Mathematical Society 42, no. 3 (December 1990): 369–82. http://dx.doi.org/10.1017/s0004972700028537.

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50

Zeng, Renying. "On Sub Convexlike Optimization Problems." Mathematics 11, no. 13 (June 29, 2023): 2928. http://dx.doi.org/10.3390/math11132928.

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Анотація:

In this paper, we show that the sub convexlikeness and subconvexlikeness defined by V. Jeyakumar are equivalent in locally convex topological spaces. We also deal with set-valued vector optimization problems and obtained vector saddle-point theorems and vector Lagrangian theorems.

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