scholarly journals A generalization on character Connes-amenability

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4059-4070
Author(s):  
Behrouz Shojaee
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Continuous Homomorphism ◽  
Current Paper ◽  
Hereditary Properties ◽  
Connes Amenability ◽  
Dual Banach Algebra

In the current paper, we introduce the concepts of left ?-approximate Connes-amenability and left character approximate Connes-amenability of a dual Banach algebra A that ? is a ?*-continuous homomorphism fromAto C. We also characterize left ?-approximate Connes-amenability ofAin terms of certain derivations and study some hereditary properties for such Banach algebras. Some examples show that these new notions are different from approximate Connes-amenability and left character Connesamenability for dual Banach algebras.

scholarly journals Johnson pseudo-Connes amenability of dual Banach algebras

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 551-559
Author(s):  
Amir Sahami ◽  
Seyedeh Shariati ◽  
Abdolrasoul Pourabbas
Keyword(s):  
Compact Group ◽  
Finite Index ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Hereditary Properties ◽  
Connes Amenability

We introduce the notion of Johnson pseudo-Connes amenability for dual Banach algebras. We study the relation between this new notion with the various notions of Connes amenability like Connes amenability, approximate Connes amenability and pseudo Connes amenability. We also investigate some hereditary properties of this new notion. We prove that for a locally compact group G,M(G) is Johnson pseudo-Connes amenable if and only if G is amenable. Also we show that for every non-empty set I,MI(C) under this new notion is forced to have a finite index. Finally, we provide some examples of certain dual Banach algebras and we study their Johnson pseudo-Connes amenability.

scholarly journals Derivations into annihilators of the ideals of Banach algebras

2019 ◽  
Vol 52 (1) ◽  
pp. 20-28
Author(s):  
Akram Teymouri ◽  
Abasalt Bodaghi ◽  
Davood Ebrahimi Bagha
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Weak Amenability ◽  
New Concepts ◽  
Hereditary Properties ◽  
Ideal Amenability ◽  
The Ideal

AbstractIn this article, following Gorgi and Yazdanpanah, we define two new concepts of the ideal amenability for a Banach algebra A. We compare these notions with J-weak amenability and ideal amenability, where J is a closed two-sided ideal in A. We also study the hereditary properties of quotient ideal amenability for Banach algebras. Some examples show that the concepts of A/J-weak amenability and of J-weak amenability do not coincide for Banach algebras in general.

scholarly journals Approximate Connes-biprojectivity of dual Banach algebras

2020 ◽  
pp. 2150025
Author(s):  
A. Sahami ◽  
S. F. Shariati ◽  
A. Pourabbas
Keyword(s):  
Compact Group ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Convolution Product ◽  
Locally Compact ◽  
Triangular Banach Algebras ◽  
Connes Amenability

In this paper, we introduce a notion of approximate Connes-biprojectivity for dual Banach algebras. We study the relation between approximate Connes-biprojectivity, approximate Connes amenability and [Formula: see text]-Connes amenability. We propose a criterion to show that certain dual triangular Banach algebras are not approximately Connes-biprojective. Next, we show that for a locally compact group [Formula: see text], the Banach algebra [Formula: see text] is approximately Connes-biprojective if and only if [Formula: see text] is amenable. Finally, for an infinite commutative compact group [Formula: see text], we show that the Banach algebra [Formula: see text] with convolution product is approximately Connes-biprojective, but it is not Connes-biprojective.

scholarly journals On bounded dual-valued derivations on certain Banach algebras

2009 ◽  
Vol 86 (100) ◽  
pp. 107-114
Author(s):  
A.L. Barrenechea ◽  
C.C. Peña
Keyword(s):  
Banach Algebra ◽  
Dual Space ◽  
Banach Algebras ◽  
Class D ◽  
Unitary Dual ◽  
Dual Banach Algebra

We consider the class D(U) of bounded derivations Ud?U*defined on a Banach algebra U with values in its dual space U*so that ?x,d(x)? = 0 for all x?U U. The existence of such derivations is shown, but lacking the simplest structure of an inner one. We characterize the elements of D(U) if span(U2) is dense in U or if U is a unitary dual Banach algebra.

scholarly journals Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule

2004 ◽  
Vol 95 (1) ◽  
pp. 124 ◽  
Author(s):  
Volker Runde
Keyword(s):  
Abelian Subgroup ◽  
Von Neumann Algebras ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Von Neumann ◽  
Connes Amenability ◽  
Definition Of ◽  
Dual Banach Algebra

Let $\mathcal A$ be a dual Banach algebra with predual $\mathcal A_*$ and consider the following assertions: (A) $\mathcal A$ is Connes-amenable; (B) $\mathcal A$ has a normal, virtual diagonal; (C) $\mathcal A_*$ is an injective $\mathcal A$-bimodule. For general $\mathcal A$, all that is known is that (B) implies (A) whereas, for von Neumann algebras, (A), (B), and (C) are equivalent. We show that (C) always implies (B) whereas the converse is false for $\mathcal A = M(G)$ where $G$ is an infinite, locally compact group. Furthermore, we present partial solutions towards a characterization of (A) and (B) for $\mathcal A = B(G)$ in terms of $G$: For amenable, discrete $G$ as well as for certain compact $G$, they are equivalent to $G$ having an abelian subgroup of finite index. The question of whether or not (A) and (B) are always equivalent remains open. However, we introduce a modified definition of a normal, virtual diagonal and, using this modified definition, characterize the Connes-amenable, dual Banach algebras through the existence of an appropriate notion of virtual diagonal.

scholarly journals Extension of Derivations, and Connes- Amenability of the Enveloping Dual Banach Algebra

2015 ◽  
Vol 117 (2) ◽  
pp. 258 ◽  
Author(s):  
Yemon Choi ◽  
Ebrahim Samei ◽  
Ross Stokke
Keyword(s):  
Banach Algebra ◽  
Usual Sense ◽  
Invariant Means ◽  
Connes Amenability ◽  
Extension Result ◽  
Dual Banach Algebra

If $D:A \to X$ is a derivation from a Banach algebra to a contractive, Banach $A$-bimodule, then one can equip $X^{**}$ with an $A^{**}$-bimodule structure, such that the second transpose $D^{**}: A^{**} \to X^{**}$ is again a derivation. We prove an analogous extension result, where $A^{**}$ is replaced by $\mathsf{F}(A)$, the enveloping dual Banach algebra of $A$, and $X^{**}$ by an appropriate kind of universal, enveloping, normal dual bimodule of $X$. Using this, we obtain some new characterizations of Connes-amenability of $\mathsf{F}(A)$. In particular we show that $\mathsf{F}(A)$ is Connes-amenable if and only if $A$ admits a so-called $\operatorname{WAP}$-virtual diagonal. We show that when $A=L^1(G)$, existence of a $\operatorname{WAP}$-virtual diagonal is equivalent to the existence of a virtual diagonal in the usual sense. Our approach does not involve invariant means for $G$.

On ϕ-amenability of Banach algebras

2008 ◽  
Vol 144 (1) ◽  
pp. 85-96 ◽  
Author(s):  
EBERHARD KANIUTH ◽  
ANTHONY T. LAU ◽  
JOHN PYM
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Hereditary Properties

AbstractGeneralizing the notion of left amenability for so-called F-algebras [12], we study the concept of ϕ-amenability of a Banach algebra A, where ϕ is a homomorphism from A to ℂ. We establish several characterizations of ϕ-amenability as well as some hereditary properties. In addition, some illuminating examples are given.

scholarly journals n-Weak Module Amenability of Triangular Banach Algebras

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
Abasalt Bodaghi ◽  
Ali Jabbari
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Current Paper ◽  
Module Amenability ◽  
Weak Module ◽  
Arens Regularity ◽  
Triangular Banach Algebras

AbstractLet A, B be Banach A-modules with compatible actions and M be a left Banach A- A-module and a right Banach B- A-module. In the current paper, we study module amenability, n-weak module amenability and module Arens regularity of the triangular Banach algebra -

ON ALGEBRA ISOMORPHISMS BETWEEN p-BANACH BEURLING ALGEBRAS

2021 ◽  
pp. 1-12
Author(s):  
PRAKASH A. DABHI ◽  
DARSHANA B. LIKHADA
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Discrete Groups ◽  
Discrete Semigroups ◽  
Beurling Algebras

Abstract Let $(G_1,\omega _1)$ and $(G_2,\omega _2)$ be weighted discrete groups and $0\lt p\leq 1$ . 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.

A characterization of Jordan and 5-Jordan homomorphisms between Banach algebras

2018 ◽  
Vol 11 (02) ◽  
pp. 1850021 ◽  
Author(s):  
A. Zivari-Kazempour
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Jordan Homomorphism ◽  
Jordan Homomorphisms ◽  
Unital Banach Algebra

We prove that each surjective Jordan homomorphism from a Banach algebra [Formula: see text] onto a semiprime commutative Banach algebra [Formula: see text] is a homomorphism, and each 5-Jordan homomorphism from a unital Banach algebra [Formula: see text] into a semisimple commutative Banach algebra [Formula: see text] is a 5-homomorphism.

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