Ideal amenability of module extension Banach algebras

2007 ◽  
Vol 2 ◽  
pp. 213-219
Author(s):  
M. Eshaghi Gordji ◽  
F. Habibian ◽  
A. Rejali
Keyword(s):  
Banach Algebras ◽  
Module Extension ◽  
Ideal Amenability

scholarly journals Derivations on the module extension Banach algebras

2021 ◽  
Vol 73 (4) ◽  
pp. 566-576
Author(s):  
A. Bodaghi ◽  
A. Teymouri ◽  
D. Ebrahimi Bagha
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Closed Ideal ◽  
Closed Submodule ◽  
Module Extension ◽  
Necessary And Sufficient ◽  
Ideal Amenability

UDC 517.986 We correct some results presented in [M. Eshaghi Gordji, F. Habibian, A. Rejali, <em> Ideal amenability of module extension Banach algebras</em>, Int. J. Contemp. Math. Sci.,  <strong>2</strong>, No. 5, 213–219 (2007)] and, using the obtained consequences, we find necessary and sufficient conditions for the module extension to be -weakly amenable, where is a closed ideal of the Banach algebra and is a closed -submodule of the Banach -bimodule We apply this result to the module extension where are two Banach -bimodules.

scholarly journals Ideal amenability of second duals of Banach algebras

2007 ◽  
Vol 2 ◽  
pp. 765-770
Author(s):  
M. Eshaghi Gordji ◽  
F. Habibian ◽  
B. Hayati
Keyword(s):  
Banach Algebras ◽  
Ideal Amenability

scholarly journals ON n-IDEAL AMENABILITY OF CERTAIN BANACH ALGEBRAS

2011 ◽  
Vol 86 (1) ◽  
pp. 90-99 ◽  
Author(s):  
ZEINAB KAMALI ◽  
MEHDI NEMATI
Keyword(s):  
Banach Algebras ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Ideal Amenability ◽  
Segal Algebras

AbstractIn this paper we consider some notions of amenability such as ideal amenability, n-ideal amenability and approximate n-ideal amenability. The first two were introduced and studied by Gordji, Yazdanpanah and Memarbashi. We investigate some properties of certain Banach algebras in each of these classes. Results are also given for Segal algebras on locally compact groups.

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.

THE BOCHNER–SCHOENBERG-EBERLEIN PROPERTY OF EXTENSIONS OF BANACH ALGEBRAS AND BANACH MODULES

2021 ◽  
pp. 1-12
Author(s):  
NASRIN ALIZADEH ◽  
ALI EBADIAN ◽  
SAEID OSTADBASHI ◽  
ALI JABBARI
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Banach Modules ◽  
Module Extension

Abstract Let A be a Banach algebra and let X be a Banach A-bimodule. We consider the Banach algebra ${A\oplus _1 X}$ , where A is a commutative Banach algebra. We investigate the Bochner–Schoenberg–Eberlein (BSE) property and the BSE module property on $A\oplus _1 X$ . We show that the module extension Banach algebra $A\oplus _1 X$ is a BSE Banach algebra if and only if A is a BSE Banach algebra and $X=\{0\}$ . Furthermore, we consider $A\oplus _1 X$ as a Banach $A\oplus _1 X$ -module and characterise the BSE module property on $A\oplus _1 X$ . We show that $A\oplus _1 X$ is a BSE Banach $A\oplus _1 X$ -module if and only if A and X are BSE Banach A-modules.

scholarly journals Arens Regularity of Certain Class of Banach Algebras

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Abbas Sahleh ◽  
Abbas Zivari-Kazempour
Keyword(s):  
Banach Algebra ◽  
Dual Space ◽  
Banach Algebras ◽  
Arens Regularity ◽  
Left And Right ◽  
Module Extension

We study Arens regularity of the left and right module actions of on , where is thenth dual space of a Banach algebra , and then investigate (quotient) Arens regularity of as a module extension of Banach algebras.

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