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Journal articles on the topic 'Banach algebras'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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1

Nasr-Isfahani, R. "Fixed point characterization of left amenable Lau algebras." International Journal of Mathematics and Mathematical Sciences 2004, no. 62 (2004): 3333–38. http://dx.doi.org/10.1155/s0161171204310446.

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The present paper deals with the concept of left amenability for a wide range of Banach algebras known as Lau algebras. It gives a fixed point property characterizing left amenable Lau algebras𝒜in terms of left Banach𝒜-modules. It also offers an application of this result to some Lau algebras related to a locally compact groupG, such as the Eymard-Fourier algebraA(G), the Fourier-Stieltjes algebraB(G), the group algebraL1(G), and the measure algebraM(G). In particular, it presents some equivalent statements which characterize amenability of locally compact groups.

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2

Ludkovsky, S., and B. Diarra. "Spectral integration and spectral theory for non-Archimedean Banach spaces." International Journal of Mathematics and Mathematical Sciences 31, no. 7 (2002): 421–42. http://dx.doi.org/10.1155/s016117120201150x.

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Banach algebras over arbitrary complete non-Archimedean fields are considered such that operators may be nonanalytic. There are different types of Banach spaces over non-Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebraℒ(E)of the continuous linear operators on a free Banach spaceEgenerated by projectors. We investigate the spectral integration of non-Archimedean Banach algebras. We define a spectral measure and prove several properties. We prove the non-Archimedean analog of Stone theorem. It also contains the case ofC-algebrasC∞(X,𝕂). We prove a particular case of a representation of aC-algebra with the help of aL(Aˆ,μ,𝕂)-projection-valued measure. We consider spectral theorems for operators and families of commuting linear continuous operators on the non-Archimedean Banach space.

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3

Yoon Yang, Seo, Abasalt Bodaghi, and Kamel Ariffin Mohd Atan. "Approximate Cubic ∗-Derivations on Banach ∗-Algebras." Abstract and Applied Analysis 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/684179.

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4

Ludkowski, Sergey Victor. "Algebras of Vector Functions over Normed Fields." Inventions 7, no. 4 (November 14, 2022): 102. http://dx.doi.org/10.3390/inventions7040102.

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This article is devoted to study of vector functions in Banach algebras and Banach spaces over normed fields. A structure of their Banach algebras is investigated. Banach algebras of vector functions with values in ∗-algebras, finely regular algebras, B∗-algebras, and operator algebras are scrutinized. An approximation of vector functions is investigated. The realizations of these algebras by operator algebras are studied.

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5

Ebadian, A., and A. Jabbari. "ГИПЕРТАУБЕРОВЫ АЛГЕБРЫ, ОПРЕДЕЛЕННЫЕ ГОМОМОРФИЗМОМ БАНАХОВОЙ АЛГЕБРЫ." Вестник КРАУНЦ. Физико-математические науки, no. 1 (May 4, 2019): 18–28. http://dx.doi.org/10.26117/2079-6641-2019-26-1-18-28.

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Let A and B be Banach algebras and T: B→A be a continuous homomorphism. We consider left multipliers from A×TB into its the first dual i.e., A*×B* and we show that A×TB is a hyper-Tauberian algebra if and only if A and B are hyper-Tauberian algebras. Пусть A и B – банаховы алгебры, а T: B→A – непрерывный гомоморфизм. Мы рассматриваем левые мультипликаторы из A×TB в его первое двойственное, т.е. A*×B*, и показываем, что A×TB является гипертауберовой алгеброй тогда и только тогда, когда A и B являются гипертауберовыми алгебрами.

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6

Srivastava, Neeraj, S. Bhattacharya, and S. N. Lal. "2-normed algebras-II." Publications de l'Institut Math?matique (Belgrade) 90, no. 104 (2011): 135–43. http://dx.doi.org/10.2298/pim1104135s.

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In the first part of the paper [5], we gave a new definition of real or complex 2-normed algebras and 2-Banach algebras. Here we give two examples which establish that not all 2-normed algebras are normable and a 2-Banach algebra need not be a 2-Banach space. We conclude by deriving a new and interesting spectral radius formula for 1-Banach algebras from the basic properties of 2-Banach algebras and thus vindicating our definitions of 2-normed and 2-Banach algebras given in [5].

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7

BATKUNDE, HARMANUS, and Elvinus R. Persulessy. "ALJABAR-C* DAN SIFATNYA." BAREKENG: Jurnal Ilmu Matematika dan Terapan 6, no. 1 (March 1, 2012): 19–22. http://dx.doi.org/10.30598/barekengvol6iss1pp19-22.

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These notes in this paper form an introductory of C*-algebras and its properties. Some results on more general Banach algebras and C*-algebras, are included. We shall prove and discuss basic properties of Banach Algebras, C*-algebras, and commutative C*-algebras. We will also give important examples for Banach Algebras, C*-algebras, and commutative C*-algebras.

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8

Maouche, Abdelaziz. "Gleason-Kahane-Zelazko Theorem in Jordan Banach algebras." Gulf Journal of Mathematics 16, no. 2 (April 12, 2024): 39–51. http://dx.doi.org/10.56947/gjom.v16i2.1868.

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We review the celebrated Gleason-Kahane-Zelazko and Kowalski-Slodkowski theorems from the setting of associative Banach algebras to the wider class of nonassociative Jordan Banach algebras. We introduce the notion of almost multiplicative linear functionals in Jordan Banach algebras and prove a theorem extending a former result of B.E. Johnson for Banach algebras by employing the more recent concept of condition spectrum. We show how to rediscover the Gleason-Kahane-Zelazko theorem for Jordan Banach algebras from the corresponding version for almost multiplicative linear functionals.

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9

Gourdeau, Frédéric. "Amenability of Lipschitz algebras." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 3 (November 1992): 581–88. http://dx.doi.org/10.1017/s0305004100071267.

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In this article, we study the amenability of Banach algebras in general, and that of Lipschitz algebras in particular. After introducing an alternative definition of amenability, we extend a result of [5], thereby proving a new characterization of amenability for Banach algebras. This characterization relates the amenability of a Banach algebra A to the space of bounded homomorphisms from A into another Banach algebra B (Theorem 4). This result allows us to solve the problem of amenability for virtually all Lipschitz algebras (of complex or Banach algebra valued functions), a class of algebras which has been studied in [2], [4] and [5].

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10

Khodakarami, Wania, Hoger Ghahramani, and Esmaeil Feizi. "Relative amenability of Banach algebras." Filomat 36, no. 6 (2022): 2091–103. http://dx.doi.org/10.2298/fil2206091k.

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Let A be a Banach algebra and I be a closed ideal of A. We say that A is amenable relative to I, if A/I is an amenable Banach algebra. We study the relative amenability of Banach algebras and investigate the relative amenability of triangular Banach algebras and Banach algebras associated to locally compact groups. We generalize some of the previous known results by applying the concept of relative amenability of Banach algebras, especially, we present a generalization of Johnson?s theorem in the concept of relative amenability.

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11

DIXON, P. G. "Graded Banach algebras associated with varieties of Banach algebras." Mathematical Proceedings of the Cambridge Philosophical Society 135, no. 3 (November 2003): 469–79. http://dx.doi.org/10.1017/s0305004103006972.

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12

Schmitt, Lothar M. "Quotients of local Banach algebras are local Banach algebras." Publications of the Research Institute for Mathematical Sciences 27, no. 6 (1991): 837–43. http://dx.doi.org/10.2977/prims/1195169002.

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13

Essmaili, Morteza, Ali Rejali, and Azam Marzijarani. "Characterization of homological properties of θ-Lau product of Banach algebras." Filomat 35, no. 1 (2021): 37–46. http://dx.doi.org/10.2298/fil2101037e.

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Let A and B be two Banach algebras and ?? ?(B): In this paper, we investigate biprojectivity and biflatness of ?-Lau product of Banach algebras A x? B. Indeed, we show that A x? B is biprojective if and only if A is contractible and B is biprojective. This generalizes some known results. Moreover, we characterize biflatness of ?-Lau product of Banach algebras under some conditions. As an application, we give an example of biflat Banach algebras A and X such that the generalized module extension Banach algebra X o A is not biflat. Finally, we characterize pseudo-contractibility of ?-Lau product of Banach algebras and give an affirmative answer to an open question.

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14

NASR-ISFAHANI, RASOUL, and MEHDI NEMATI. "ESSENTIAL CHARACTER AMENABILITY OF BANACH ALGEBRAS." Bulletin of the Australian Mathematical Society 84, no. 3 (November 1, 2011): 372–86. http://dx.doi.org/10.1017/s0004972711002620.

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AbstractFor a Banach algebra 𝒜 and a character ϕ on 𝒜, we introduce and study the notion of essential ϕ-amenability of 𝒜. We give some examples to show that the class of essentially ϕ-amenable Banach algebras is larger than that of ϕ-amenable Banach algebras introduced by Kaniuth et al. [‘On ϕ-amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc.144 (2008), 85–96]. Finally, we characterize the essential ϕ-amenability of various Banach algebras related to locally compact groups.

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15

Allan, Graham R., and Theodore W. Palmer. "Banach Algebras and the General Theory of Algebras. Volume 1: Algebras and Banach Algebras." Mathematical Gazette 80, no. 489 (November 1996): 635. http://dx.doi.org/10.2307/3618560.

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16

Heo, Jaeseong. "Symmetric operator amenability of operator algebras." Filomat 36, no. 10 (2022): 3471–78. http://dx.doi.org/10.2298/fil2210471h.

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Using the notion of a symmetric virtual diagonal for a Banach algebra, we prove that a Banach algebra is symmetrically amenable if its second dual is symmetrically amenable. We introduce symmetric operator amenability in the category of completely contractive Banach algebras as an operator algebra analogue of symmetric amenability of Banach algebras. We give some equivalent formulations of symmetric operator amenability of completely contractive Banach algebras and investigate some hereditary properties of symmetric operator amenable algebras. We show that amenability of locally compact groups is equivalent to symmetric operator amenability of its Fourier algebra. Finally, we discuss about Jordan derivation on symmetrically operator amenable algebras.

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17

Alabkary, Narjes. "Hyper-instability of Banach algebras." AIMS Mathematics 9, no. 6 (2024): 14012–25. http://dx.doi.org/10.3934/math.2024681.

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<abstract><p>In this paper, we introduce and study the concept of hyper-instability as a strong version of multiplicative instability. This concept provides a powerful tool to study the multiplicative instability of Banach algebras. It replaces the condition of the iterated limits in the definition of multiplicative instability with conditions that are easier to examine. In particular, special conditions are suggested for Banach algebras that admit bounded approximate identities. Moreover, these conditions are preserved under isomorphisms. This enlarges the class of studied Banach algebras. We prove that many interesting Banach algebras are hyper-unstable, such as $ C^* $-algebras, Fourier algebras, and the algebra of compact operators on Banach spaces, each under certain conditions.</p></abstract>

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18

Takahasi, Sin-Ei. "An extension of Helson-Edwards theorem to Banach Modules." International Journal of Mathematics and Mathematical Sciences 14, no. 2 (1991): 227–32. http://dx.doi.org/10.1155/s0161171291000248.

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An extension of the Helson-Edwards theorem for the group algebras to Banach modules over commutative Banach algebras is given. This extension can be viewed as a generalization of Liu-Rooij-Wang's result for Banach modules over the group algebras.

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19

Ebadian, Ali, and Ali Jabbari. "Ultrapowers of Banach algebras." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 9, no. 3 (2022): 527–41. http://dx.doi.org/10.21638/spbu01.2022.313.

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In this paper, we consider ultrapowers of Banach algebras as Banach algebras and the product (J,U) on the second dual of Banach algebras. For a Banach algebra A, we show that if there is a continuous derivation from A into itself, then there is a continuous derivation from (A**,(J,U)) into it. Moreover, we show that if there is a continuous derivation from A into X**, where X is a Banach A-bimodule, then there is a continuous derivation from A into ultrapower of X i. e., (X)U . Ultra (character) amenability of Banach algebras is investigated and it will be shown that if every continuous derivation from A into (X)U is inner, then A is ultra amenable. Some results related to left (resp. right) multipliers on (A**,(J,U)) are also given.

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20

GORDJI, M. ESHAGHI, R. KHODABAKHSH, and H. KHODAEI. "ON APPROXIMATE n-ARY DERIVATIONS." International Journal of Geometric Methods in Modern Physics 08, no. 03 (May 2011): 485–500. http://dx.doi.org/10.1142/s0219887811005245.

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C. Park et al. proved the stability of homomorphisms and derivations in Banach algebras, Banach ternary algebras, C*-algebras, Lie C*-algebras and C*-ternary algebras. In this paper, we improve and generalize some results concerning derivations. We first introduce the following generalized Jensen functional equation [Formula: see text] and using fixed point methods, we prove the stability of n-ary derivations and n-ary Jordan derivations in n-ary Banach algebras. Secondly, we study this functional equation with *-n-ary derivations in C*-n-ary algebras.

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21

Miller, John Boris. "Strictly real Banach algebras." Bulletin of the Australian Mathematical Society 47, no. 3 (June 1993): 505–19. http://dx.doi.org/10.1017/s000497270001532x.

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A complex Banach algebra is a complexification of a real Banach algebra if and only if it carries a conjugation operator. We prove a uniqueness theorem concerning strictly real selfconjugate subalgebras of a given complex algebra. An example is given of a complex Banach algebra carrying two distinct but commuting conjugations, whose selfconjugate subalgebras are both strictly real. The class of strictly real Banach algebras is shown to be a variety, and the manner of their generation by suitable elements is proved. A corollary describes some strictly real subalgebras in Hermitian Banach star algebras, including C* algebras.

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22

Gordji, Madjid Eshaghi. "Nearly Ring Homomorphisms and Nearly Ring Derivations on Non-Archimedean Banach Algebras." Abstract and Applied Analysis 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/393247.

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We prove the generalized Hyers-Ulam stability of homomorphisms and derivations on non-Archimedean Banach algebras. Moreover, we prove the superstability of homomorphisms on unital non-Archimedean Banach algebras and we investigate the superstability of derivations in non-Archimedean Banach algebras with bounded approximate identity.

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23

El Harti, R. "The structure of a subclass of amenable banach algebras." International Journal of Mathematics and Mathematical Sciences 2004, no. 55 (2004): 2963–69. http://dx.doi.org/10.1155/s0161171204401069.

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We give sufficient conditions that allow contractible (resp., reflexive amenable) Banach algebras to be finite-dimensional and semisimple algebras. Moreover, we show that any contractible (resp., reflexive amenable) Banach algebra in which every maximal left ideal has a Banach space complement is indeed a direct sum of finitely many full matrix algebras. Finally, we characterize Hermitian*-algebras that are contractible.

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24

GHAHRAMANI, F., and Y. ZHANG. "Pseudo-amenable and pseudo-contractible Banach algebras." Mathematical Proceedings of the Cambridge Philosophical Society 142, no. 1 (January 2007): 111–23. http://dx.doi.org/10.1017/s0305004106009649.

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AbstractWe introduce and study two new notions of amenability for Banach algebras. In particular we compare these notions with some of those studied earlier. We show that several classes of Banach algebras, including certain Banach algebras related to locally compact groups, are responsive to these notions.

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25

Yost, David. "Strictly Convex Banach Algebras." Axioms 10, no. 3 (September 11, 2021): 221. http://dx.doi.org/10.3390/axioms10030221.

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We discuss two facets of the interaction between geometry and algebra in Banach algebras. In the class of unital Banach algebras, there is essentially one known example which is also strictly convex as a Banach space. We recall this example, which is finite-dimensional, and consider the open question of generalising it to infinite dimensions. In C∗-algebras, we exhibit one striking example of the tighter relationship that exists between algebra and geometry there.

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26

Tomiuk, Bohdan, and Bertram Yood. "Incomplete normed algebra norms on Banach algebras." Studia Mathematica 95, no. 2 (1989): 119–32. http://dx.doi.org/10.4064/sm-95-2-119-132.

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27

LAWSON, P., and C. J. READ. "Approximate amenability of Fréchet algebras." Mathematical Proceedings of the Cambridge Philosophical Society 145, no. 2 (September 2008): 403–18. http://dx.doi.org/10.1017/s0305004108001473.

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AbstractThe notion of approximate amenability was introduced by Ghahramani and Loy, in the hope that it would yield Banach algebras without bounded approximate identity which nonetheless had a form of amenability. So far, however, all known approximately amenable Banach algebras have bounded approximate identities (b.a.i.). In this paper we define approximate amenability and contractibility of Fréchet algebras, and we prove the analogue of the result for Banach algebras that these properties are equivalent. We give examples of Fréchet algebras which are approximately contractible, but which do not have a bounded approximate identity. For a good many Fréchet algebras without b.a.i., we find either that the algebra is approximately amenable, or it is “obviously” not approximately amenable because it has continuous point derivations. So the situation for Fréchet algebras is quite close to what was hoped for Banach algebras.

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28

Guerrero, Julio Becerra, Simon Cowell, Ángel Rodríguez Palacios, and Geoffrey V. Wood. "Unitary Banach algebras." Studia Mathematica 162, no. 1 (2004): 25–51. http://dx.doi.org/10.4064/sm162-1-3.

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29

Li, Bingren, and Pingkwan Tam. "Real Banach ✶ Algebras." Acta Mathematica Sinica, English Series 16, no. 3 (July 2000): 469–86. http://dx.doi.org/10.1007/pl00011555.

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30

Li, Bingren, and Pingkwan Tam. "Real Banach ✶ Algebras." Acta Mathematica Sinica 16, no. 3 (July 2000): 469–86. http://dx.doi.org/10.1007/s101140000062.

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31

Foulis, David J., and Sylvia Pulmannov. "Banach Synaptic Algebras." International Journal of Theoretical Physics 57, no. 4 (December 14, 2017): 1103–19. http://dx.doi.org/10.1007/s10773-017-3641-y.

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32

Alaminos, J., M. Brešar, Š. Špenko, and A. R. Villena. "Orthogonally Additive Polynomials and Orthosymmetric Maps in Banach Algebras with Properties 𝔸 and 𝔹." Proceedings of the Edinburgh Mathematical Society 59, no. 3 (December 15, 2015): 559–68. http://dx.doi.org/10.1017/s0013091515000383.

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AbstractThis paper considers Banach algebras with properties 𝔸 or 𝔹, introduced recently by Alaminos et al. The class of Banach algebras satisfying either of these two properties is quite large; in particular, it includes C*-algebras and group algebras on locally compact groups. Our first main result states that a continuous orthogonally additive n-homogeneous polynomial on a commutative Banach algebra with property 𝔸 and having a bounded approximate identity is of a standard form. The other main results describe Banach algebras A with property 𝔹 and having a bounded approximate identity that admit non-zero continuous symmetric orthosymmetric n-linear maps from An into ℂ.

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33

Grønbæk, Niels, and George A. Willis. "Embedding Nilpotent Finite Dimensional Banach Algebras into Amenable Banach Algebras." Journal of Functional Analysis 145, no. 1 (April 1997): 99–107. http://dx.doi.org/10.1006/jfan.1996.3025.

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34

İnceboz, Hülya, and Berna Arslan. "The first module (σ,τ)-cohomology group of triangular Banach algebras of order three." Journal of Algebra and Its Applications 17, no. 12 (December 2018): 1850225. http://dx.doi.org/10.1142/s0219498818502250.

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The notion of module amenability for a class of Banach algebras, which could be considered as a generalization of Johnson’s amenability, was introduced by Amini in [Module amenability for semigroup algebras, Semigroup Forum 69 (2004) 243–254]. The weak module amenability of the triangular Banach algebra [Formula: see text], where [Formula: see text] and [Formula: see text] are Banach algebras (with [Formula: see text]-module structure) and [Formula: see text] is a Banach [Formula: see text]-module, is studied by Pourabbas and Nasrabadi in [Weak module amenability of triangular Banach algebras, Math. Slovaca 61(6) (2011) 949–958], and they showed that the weak module amenability of [Formula: see text] triangular Banach algebra [Formula: see text] (as an [Formula: see text]-bimodule) is equivalent with the weak module amenability of the corner algebras [Formula: see text] and [Formula: see text] (as Banach [Formula: see text]-bimodules). The main aim of this paper is to investigate the module [Formula: see text]-amenability and weak module [Formula: see text]-amenability of the triangular Banach algebra [Formula: see text] of order three, where [Formula: see text] and [Formula: see text] are [Formula: see text]-module morphisms on [Formula: see text]. Also, we give some results for semigroup algebras.

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35

Dedania, H. V., and H. J. Kanani. "Some Banach algebra properties in the Cartesian product of Banach algebras." Annals of Functional Analysis 5, no. 1 (2014): 51–55. http://dx.doi.org/10.15352/afa/1391614568.

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36

Tomiuk, B. J. "Biduals of Banach algebras which are ideals in a Banach algebra." Acta Mathematica Hungarica 52, no. 3-4 (September 1988): 255–63. http://dx.doi.org/10.1007/bf01951571.

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37

DABHI, PRAKASH A., and DARSHANA B. LIKHADA. "ON ALGEBRA ISOMORPHISMS BETWEEN p-BANACH BEURLING ALGEBRAS." Bulletin of the Australian Mathematical Society 104, no. 2 (January 11, 2021): 308–19. http://dx.doi.org/10.1017/s0004972720001392.

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AbstractLet $(G_1,\omega _1)$ and $(G_2,\omega _2)$ be weighted discrete groups and $0<p\leq 1$ . We characterise biseparating bicontinuous algebra isomorphisms on the p-Banach algebra $\ell ^p(G_1,\omega _1)$ . We also characterise bipositive and isometric algebra isomorphisms between the p-Banach algebras $\ell ^p(G_1,\omega _1)$ and $\ell ^p(G_2,\omega _2)$ and isometric algebra isomorphisms between $\ell ^p(S_1,\omega _1)$ and $\ell ^p(S_2,\omega _2)$ , where $(S_1,\omega _1)$ and $(S_2,\omega _2)$ are weighted discrete semigroups.

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38

Runde, Volker. "Automatic continuity and second order cohomology." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 68, no. 2 (April 2000): 231–43. http://dx.doi.org/10.1017/s1446788700001968.

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AbstractMany Banach algebras A have the property that, although there are discontinuous homomorphisms from A into other Banach algebras, every homomorphism from A into another Banach algebra is automatically continuous on a dense subspace—preferably, a subalgebra—of A. Examples of such algebras are C*-algebras and the group algebras L1(G), where G is a locally compact, abelian group. In this paper, we prove analogous results for , where E is a Banach space, and . An important rôle is played by the second Hochschild cohomology group of and , respectively, with coefficients in the one-dimensional annihilator module. It vanishes in the first case and has linear dimension one in the second one.

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39

POURMAHMOOD-AGHABABA, HASAN. "APPROXIMATELY BIPROJECTIVE BANACH ALGEBRAS AND NILPOTENT IDEALS." Bulletin of the Australian Mathematical Society 87, no. 1 (May 22, 2012): 158–73. http://dx.doi.org/10.1017/s0004972712000251.

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AbstractBy introducing a new notion of approximate biprojectivity we show that nilpotent ideals in approximately amenable or pseudo-amenable Banach algebras, and nilpotent ideals with the nilpotency degree larger than two in biflat Banach algebras cannot have the special property which we call ‘property (𝔹)’ (Definition 5.2 below) and hence, as a consequence, they cannot be boundedly approximately complemented in those Banach algebras.

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40

Abtahi, Fatemeh, Somaye Rahnama, and Ali Rejali. "ϕ-amenability and character amenability of Fréchet algebras." Forum Mathematicum 30, no. 6 (November 1, 2018): 1413–35. http://dx.doi.org/10.1515/forum-2016-0116.

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AbstractRight φ-amenability and right character amenability have been introduced for Banach algebras. Here, these concepts will be generalized for Fréchet algebras. Then some of the previous available results about right φ-amenability and right character amenability for the case of Banach algebras will be verified for Fréchet algebras. Related results about Segal Fréchet algebras are provided.

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41

Liau, Pao-Kuei, and Cheng-Kai Liu. "Skew Derivations in Banach Algebras." Proceedings of the Edinburgh Mathematical Society 58, no. 3 (June 10, 2015): 683–96. http://dx.doi.org/10.1017/s001309151500005x.

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42

PIRKOVSKII, A. YU. "Approximate characterizations of projectivity and injectivity for Banach modules." Mathematical Proceedings of the Cambridge Philosophical Society 143, no. 2 (September 2007): 375–85. http://dx.doi.org/10.1017/s0305004107000163.

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AbstractWe characterize projective and injective Banach modules in approximate terms, generalizing thereby a characterization of contractible Banach algebras given by F. Ghahramani and R. J. Loy. As a corollary, we show that each uniformly approximately amenable Banach algebra is amenable. Some applications to homological dimensions of Banach modules and algebras are also given.

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43

Inoue, Jyunji, and Sin-Ei Takahasi. "Segal algebras in commutative Banach algebras." Rocky Mountain Journal of Mathematics 44, no. 2 (April 2014): 539–89. http://dx.doi.org/10.1216/rmj-2014-44-2-539.

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44

Ghorbai, M., and Davood Ebrahimi Bagha. "Amenability of A⊕_T X as an extension of Banach algebra." Mathematica Montisnigri 49 (2020): 39–48. http://dx.doi.org/10.20948/mathmontis-2020-49-3.

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Let 𝐴𝐴,𝑋𝑋,𝔘𝔘 be Banach algebras and 𝐴𝐴 be a Banach 𝔘𝔘-bimodule also 𝑋𝑋 be a Banach 𝐴𝐴−𝔘𝔘-module. In this paper we study the relation between module amenability, weak module amenability and module approximate amenability of Banach algebra 𝐴𝐴⊕𝑇𝑇𝑋𝑋 and that of Banach algebras 𝐴𝐴,𝑋𝑋. Where 𝑇𝑇: 𝐴𝐴×𝐴𝐴→𝑋𝑋 is a bounded bi-linear mapping with specificconditions.

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45

Bae, Jae-Hyeong, Ick-Soon Chang, and Hark-Mahn Kim. "Almost Generalized Derivation on Banach Algebras." Mathematics 10, no. 24 (December 14, 2022): 4754. http://dx.doi.org/10.3390/math10244754.

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We take into consideration generalized derivations. First, we study the stability of generalized derivations on Banach algebras under consideration. Then we prove some theorems involving approximate generalized derivations on Banach algebras. These results can be applied to C*-algebras.

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46

Abel, Mati. "Dense subalgebras in noncommutative Jordan topological algebras." Acta et Commentationes Universitatis Tartuensis de Mathematica 1 (December 31, 1996): 65–70. http://dx.doi.org/10.12697/acutm.1996.01.07.

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Wilansky conjectured in [12] that normed dense Q-algebras are full subalgebras of Banach algebras. Beddaa and Oudadess proved in [2] that Wilansky’s conjecture was true. They showed that k-normed Q-algebras are full subalgebras of k-Banach algebras for each k∈(0,1]. Moreover, J. Pérez, L. Rico and A. Rodríguez showed in [8], Theorem 4, that this was also true in the case of noncommutative Jordan-Banach algebras. In the present paper this problem has been studied in a more general case. It is proved that all dense Q-subalgebras of topological algebras and of noncommutative Jordan topological algebras with continuous multiplication are full subalgebras. Some equivalent conditions that a dense subalgebra would be a Q-algebra (in subspace topology) in Q-algebras and in nonassociative Jordan Q-algebras with continuous multiplication are given.

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47

Aupetit, Bernard. "Spectrum-Preserving Linear Mappings between Banach Algebras or Jordan-Banach Algebras." Journal of the London Mathematical Society 62, no. 3 (December 2000): 917–24. http://dx.doi.org/10.1112/s0024610700001514.

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48

Roh, Jaiok, and Ick-Soon Chang. "Approximate Derivations with the Radical Ranges of Noncommutative Banach Algebras." Abstract and Applied Analysis 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/594075.

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We consider the derivations on noncommutative Banach algebras, and we will first study the conditions for a derivation on noncommutative Banach algebra. Then, we examine the stability of functional inequalities with a derivation. Finally, we take the derivations with the radical ranges on noncommutative Banach algebras.

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49

Burgos, M., A. C. Márquez-García, and A. Morales-Campoy. "Approximate Preservers on Banach Algebras andC*-Algebras." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/757646.

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The aim of the present paper is to give approximate versions of Hua’s theorem and other related results for Banach algebras andC*-algebras. We also study linear maps approximately preserving the conorm between unitalC*-algebras.

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50

Boo, Deok-Hoon, Hassan Azadi Kenary, and Choonkil Park. "FUNCTIONAL EQUATIONS IN BANACH MODULES AND APPROXIMATE ALGEBRA HOMOMORPHISMS IN BANACH ALGEBRAS." Korean Journal of Mathematics 19, no. 1 (March 30, 2011): 33–52. http://dx.doi.org/10.11568/kjm.2011.19.1.033.

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