Relevant bibliographies by topics / Locally convex topological vector space

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Locally convex topological vector space'

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Published: 6 September 2023

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Journal articles on the topic "Locally convex topological vector space"

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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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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Locally convex topological vector space"

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Vera, Mendoza Rigoberto. "Linear operations on locally convex topological vector spaces." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186699.

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Our purpose is to extend, to the class of linear operators on a locally convex space, some of the results of spectral theory. In order to do this we had to introduce some topologies on the space of operators that are not locally convex. These topologies are of interest in their own right, and have proved useful in enabling us to attain our goal. There is an important class of topological vector spaces named ab-spaces (almost bornological spaces), but there are not too many facts about them. We briefly discuss some new results and give a characterization of those spaces in Chapter 3.
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Griesan, Raymond William. "Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184510.

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Metric topologies can be viewed as one-dimensional measures. This dissertation is a topological study of two-dimensional measures. Attention is focused on locally convex vector topologies on infinite dimensional real spaces. A nabla (referred to in the literature as a 2-norm) is the analogue of a norm which assigns areas to the parallelograms. Nablas are defined for the classical normed spaces and techniques are developed for defining nablas on arbitrary spaces. The work here brings out a strong connection with tensor and wedge products. Aside from the normable theory, it is shown that nabla topologies need not be metrizable or Mackey. A class of concretely given non-Mackey nablas on the ℓp and Lp spaces is introduced and extensively analyzed. Among other results it is found that the topological dual of ℓ₁ with respect to these nabla topologies is C₀, one of the spaces infamous for having no normed predual. Also, a connection is made with the theory of two-norm convergence (not to be confused with 2-norms). In addition to the hard analysis on the classical spaces, a duality framework from which to study the softer aspects is introduced. This theory is developed in analogy with polar duality. The ideas corresponding to barrelledness, quasi-barrelledness, equicontinuity and so on are developed. This dissertation concludes with a discussion of angles in arbitrary normed spaces and a list of open questions.
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Cavalcante, Wasthenny Vasconcelos. "Espaços Vetoriais Topológicos." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/9277.

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Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-17T14:00:23Z No. of bitstreams: 1 arquivototal.pdf: 1661057 bytes, checksum: 913a7f671e2e028b60d14a02274f932a (MD5)
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In this work we investigate the concept of topological vector spaces and their properties. In the rst chapter we present two sections of basic results and in the other sections we present a more general study of such spaces. In the second chapter we restrict ourselves to the real scalar eld and we study, in the context of locally convex spaces, the Hahn-Banach and Banach-Alaoglu theorems. We also build the weak, weak-star, of bounded convergence and of pointwise convergence topologies. Finally we investigate the Theorem of Banach-Steinhauss, the Open Mapping Theorem and the Closed Graph Theorem.
Neste trabalho, estudamos o conceito de espa cos vetoriais topol ogicos e suas propriedades. No primeiro cap tulo, apresentamos duas se c~oes de resultados b asicos e, nas demais se c~oes, apresentamos um estudo sobre tais espa cos de forma mais ampla. No segundo cap tulo, restringimo-nos ao corpo dos reais e fazemos um estudo sobre os espa cos localmente convexos, o Teorema de Hahn-Banach, o Teorema de Banach- Alaoglu, constru mos as topologias fraca, fraca-estrela, da converg^encia limitada e da converg^encia pontual. Por ultimo, estudamos o Teorema da Limita c~ao Uniforme, o Teorema do Gr a co Fechado e o da Aplica c~ao Aberta no contexto mais geral dos espa cos de Fr echet.
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Baratov, Rishat. "Efficient conic decomposition and projection onto a cone in a Banach ordered space." Thesis, University of Ballarat, 2005. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/61401.

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Sehgal, Kriti. "Duality for Spaces of Holomorphic Functions into a Locally Convex Topological Vector Space." Thesis, 2018. https://etd.iisc.ac.in/handle/2005/4913.

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Consider an open subset O of the complex plane and a function f : O ÝÑ C. We understand the concept of holomorphicity of a complex-valued function. Suppose a function f defined on O takes values in a locally convex topological vector space (the complex plane is one particular example of a locally convex topological vector space). We want to study the notion of holomorphicity for f in this general setting. In the paper “Sur certains espaces de fonctions holomorphes I” [1], Alexandre Grothendieck deals with the concept of holomorphicity of vector-valued functions and duality. We read, understand, reproduce and at times fill in necessary details of the content of section 2 and a portion of section 4 of the paper. We understand the extension of Lebesgue integral to vector-valued functions on a measure space, named after I.M. Gelfand and B.J. Pettis as Gelfand-Pettis integral or Pettis integral (page 77 in [2]). Using the definition of Pettis integral and some results from complex analysis we introduce three notions of holomorphicity for the function f: holomorphicity of f on the open set O, weak derivability of f at a point zo P O and strong differentiability of f at a point zo P O. In Chapter 2 (section 2 in [1]) of this thesis, we study the conditions under which the first two notions of holomorphicity, i.e., f is holomorphic on the open set O and f is weakly derivable at every point of O coincide. Further the same conditions will imply the strong differentiability of f at each point of O. Also, we study Cauchy’s integral formula and Taylor’s expansion for vector valued holomorphic functions in Chapter 2. In section 4 of the paper “Sur certains espaces de fonctions holomorphes I” [1], for a subset of the Riemann sphere, Grothendieck introduces the space Pp ,Eq as the space of all locally holomorphic functions on vanishing at 8 if 8 P . He further considers two locally convex topological vector spaces E and F in separate duality and proves that the spaces Pp 1,Eq and Pp 2, Fq, where 1 and 2 are complementary subsets of the Riemann sphere, are in separate duality under some general conditions. In Chapter 3 of this thesis, which constitute the main portion of the thesis, we study the space Pp ,Eq and further present the argument of Grothendieck for separating duality with all details
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Helmstedt, Janet Margaret. "Closed graph theorems for locally convex topological vector spaces." Thesis, 2015. http://hdl.handle.net/10539/18010.

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A Dissertation Submitted of the Faculty of Science, University of the Witwatersrand, Johannesburg in Partial Fulfilment of the Requirements for the Degree of Master of Science
Let 4 be the class of pairs of loc ..My onvex spaces (X,V) “h ‘ch are such that every closed graph linear ,pp, 1 from X into V is continuous. It B is any class of locally . ivex l.ausdortf spaces. let & w . (X . (X.Y) e 4 for ,11 Y E B). " ‘his expository dissertation, * (B) is investigated, firstly i r arbitrary B . secondly when B is the class of C,-complete paces and thirdly whon B is a class of locally convex webbed s- .ces
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Venter, Rudolf Gerrit. "Measures and functions in locally convex spaces." Thesis, 2010. http://hdl.handle.net/2263/26547.

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In this dissertation we establish results concerning in locally convex spaces-valued measures and measurable functions. The results are explained in three parts: Firstly, we establish Liapounoff convexity-type results for locally convex space-valued measures defined on fields (of sets) or equivalently on Boolean Algebras. Liapounoff convexity-type theorems concern the compactness and convexity of the closure of the range of a vector measure. We specifically investigate such results for measures defined on fields and fields of sets with the interpolation property. We find that vector measures defined on fields with the interpolation property have properties very similar to the status quo, while similar results may not hold for vector measures defined on general fields. In the latter case we consider vector measures with properties stronger than non-atomicity, specifically, the strong continuity property. We investigate these properties and certain locally convex spaces for which some of the additivity conditions can be relaxed. In the second part of this dissertation, we firstly consider the existence of weak integrals in locally convex spaces specifically, locally convex spaces whose duals are barrelled spaces. Then, inspired by results of J. Diestel we investigate the "improved" properties of the composition of nuclear maps with a locally convex space-valued measures and functions and the properties of nuclear space-valued vector measures and functions. Amongst others we find that the measurability and integrability properties of locally convex space-valued measurable functions are improved with such a composition compared to the functions considered on their own. The third part of this dissertation involves the factorization of measurable functions. We first consider the factorization of Polish space-valued measurable functions along the lines of the famous "Doob-Dynkin's lemma", a result found in (scalar-valued) stochastic processes. This allows us to determine when, for two measurable functions, f and g it is possible to find a measurable function h, such that g= h ○ f. Similar results are established for various classes of measurable functions. We discover similar factorization results for certain multifunctions (set-valued functions) and operator-valued measurable functions. Another consequence is a factorization scheme for operators on L1(µ).
Thesis (PhD(Mathematics))--University of Pretoria, 2010.
Mathematics and Applied Mathematics
unrestricted
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Tshilombo, Mukinayi Hermenegilde. "Cohomologies on sympletic quotients of locally Euclidean Frolicher spaces." Thesis, 2015. http://hdl.handle.net/10500/19942.

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This thesis deals with cohomologies on the symplectic quotient of a Frölicher space which is locally diffeomorphic to a Euclidean Frölicher subspace of Rn of constant dimension equal to n. The symplectic reduction under consideration in this thesis is an extension of the Marsden-Weinstein quotient (also called, the reduced space) well-known from the finite-dimensional smooth manifold case. That is, starting with a proper and free action of a Frölicher-Lie-group on a locally Euclidean Frölicher space of finite constant dimension, we study the smooth structure and the topology induced on a small subspace of the orbit space. It is on this topological space that we will construct selected cohomologies such as : sheaf cohomology, Alexander-Spanier cohomology, singular cohomology, ~Cech cohomology and de Rham cohomology. Some natural questions that will be investigated are for instance: the impact of the symplectic structure on these di erent cohomologies; the cohomology that will give a good description of the topology on the objects of category of Frölicher spaces; the extension of the de Rham cohomology theorem in order to establish an isomorphism between the five cohomologies. Beside the algebraic, topological and geometric study of these new objects, the thesis contains a modern formalism of Hamiltonian mechanics on the reduced space under symplectic and Poisson structures.
Mathematical Sciences
D. Phil. (Mathematics)
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Book chapters on the topic "Locally convex topological vector space"

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Bourbaki, Nicolas. "Convex sets and locally convex spaces." In Topological Vector Spaces, 31–125. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-61715-7_2.

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Schaefer, H. H., and M. P. Wolff. "Locally Convex Topological Vector Spaces." In Topological Vector Spaces, 36–72. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1468-7_3.

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Alpay, Daniel. "Locally Convex Topological Vector Spaces." In An Advanced Complex Analysis Problem Book, 249–83. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16059-7_5.

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Gong, Xun Hua, Wan Tao Fu, and Wei Liu. "Super Efficiency for a Vector Equilibrium in Locally Convex Topological Vector Spaces." In Vector Variational Inequalities and Vector Equilibria, 233–52. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4613-0299-5_13.

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Morales, Pedro. "Properties of the set of global solutions for the cauchy problems in a locally convex topological vector space." In Ordinary and Partial Differential Equations, 276–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0074736.

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"Locally Convex Spaces and Seminorms." In Topological Vector Spaces, 133–72. Chapman and Hall/CRC, 2010. http://dx.doi.org/10.1201/9781584888673-8.

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Wong, Yau-Chuen. "Normed Spaces Associated with a Locally Convex Space." In Introductory Theory of Topological Vector Spaces, 162–69. CRC Press, 2019. http://dx.doi.org/10.1201/9780203749807-10.

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Wong, Yau-Chuen. "The Bornological Space Associated with a Locally Convex Space." In Introductory Theory of Topological Vector Spaces, 175–79. CRC Press, 2019. http://dx.doi.org/10.1201/9780203749807-12.

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Wong, Yau-Chuen. "von Neumann Bornologies and Locally Convex Topologies Determined by Convex Bornologies." In Introductory Theory of Topological Vector Spaces, 198–204. CRC Press, 2019. http://dx.doi.org/10.1201/9780203749807-15.

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"Deformations on locally convex topological vector spaces." In Interdisciplinary Mathematical Sciences, 15–24. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812709639_0003.

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Conference papers on the topic "Locally convex topological vector space"

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Kraus, Eugene J., Henk J. A. M. Heijmans, and Edward R. Dougherty. "Spatial-scaling-compatible morphological granulometries on locally convex topological vector spaces." In San Diego '92, edited by Paul D. Gader, Edward R. Dougherty, and Jean C. Serra. SPIE, 1992. http://dx.doi.org/10.1117/12.60649.

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Tsertos, Yannis. "On A-convex and lm-convex algebra structures of a locally convex space." In Topological Algebras, their Applications, and Related Topics. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc67-0-32.

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