scholarly journals A Generalization of Cyclic Amenability of Banach Algebras

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
Behrouz Shojaee ◽  
Abasalt Bodaghi
Keyword(s):  
Banach Algebra ◽  
Homomorphic Image ◽  
Banach Algebras ◽  
Amenable Banach Algebra ◽  
Weak Amenability ◽  
Simon Stevin

AbstractThis paper continues the investigation of Esslamzadeh and the first author which was begun in [ESSLAMZADEH, G. H.-SHOJAEE, B.: Approximate weak amenability of Banach algebras, Bull. Belg. Math. Soc. Simon Stevin 18 (2011), 415-429]. It is shown that homomorphic image of an approximately cyclic amenable Banach algebra is again approximately cyclic amenable. Equivalence of approximate cyclic amenability of a Banach algebra A and approximate cyclic amenability of M

Amenability of Banach algebras

1989 ◽  
Vol 105 (2) ◽  
pp. 351-355 ◽  
Author(s):  
Frédéric Gourdeau
Keyword(s):  
Banach Algebra ◽  
Metric Space ◽  
Banach Algebras ◽  
Approximate Identity ◽  
Commutative Banach Algebra ◽  
Cohomology Theory ◽  
Compact Metric Space ◽  
Amenable Banach Algebra ◽  
Second Dual

We consider the problem of amenability for a commutative Banach algebra. The question of amenability for a Banach algebra was first studied by B. E. Johnson in 1972, in [5]. The most recent contributions, to our knowledge, are papers by Bade, Curtis and Dales [1], and by Curtis and Loy [3]. In the first, amenability for Lipschitz algebras on a compact metric space K is studied. Using the fact, which they prove, that LipαK is isometrically isomorphic to the second dual of lipαK, for 0 < α < 1, they show that lipαK is not amenable when K is infinite and 0 < α < 1. In the second paper, the authors prove, without using any serious cohomology theory, some results proved earlier by Khelemskii and Scheinberg [8] using cohomology. They also discuss the amenability of Lipschitz algebras, using the result that a weakly complemented closed two-sided ideal in an amenable Banach algebra has a bounded approximate identity. Their result is stronger than that of [1].

scholarly journals Two commutative amenable non-symmetric Banach algebras

1995 ◽  
Vol 59 (2) ◽  
pp. 225-231
Author(s):  
B. E. Johnson
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Amenable Banach Algebra ◽  
Symmetric Banach Algebras

AbstractWe show that a commutative amenable Banach algebra need not be symmetric by constructing suitable examples.

scholarly journals Amenability and topological centres of the second duals of Banach algebras

2002 ◽  
Vol 65 (2) ◽  
pp. 191-197 ◽  
Author(s):  
F. Ghahramani ◽  
J. Laali
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Dual Algebra ◽  
Arens Product ◽  
Weak Amenability ◽  
Arens Regularity ◽  
Second Dual

Let  be a Banach algebra and let ** be the second dual algebra of  endowed with the first or the second Arens product. We investigate relations between amenability of ** and Arens regularity of  and the rôle topological centres in amenability of **. We also find conditions under which weak amenability of ** implies weak amenability of .

Weak Amenability of a Class of Banach Algebras

2001 ◽  
Vol 44 (4) ◽  
pp. 504-508 ◽  
Author(s):  
Yong Zhang
Keyword(s):  
Banach Algebra ◽  
Left Ideal ◽  
Banach Algebras ◽  
Approximate Identity ◽  
Dual Algebra ◽  
Weak Amenability ◽  
Second Dual

AbstractWe show that, if a Banach algebra is a left ideal in its second dual algebra and has a left bounded approximate identity, then the weak amenability of implies the (2m+ 1)-weak amenability of for all m ≥ 1.

scholarly journals Approximate characterizations of projectivity and injectivity for Banach modules

2007 ◽  
Vol 143 (2) ◽  
pp. 375-385 ◽  
Author(s):  
A. YU. PIRKOVSKII
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Amenable Banach Algebra ◽  
Banach Modules ◽  
Homological Dimensions

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.

scholarly journals ESSENTIAL AMENABILITY OF ABSTRACT SEGAL ALGEBRAS

2009 ◽  
Vol 79 (2) ◽  
pp. 319-325 ◽  
Author(s):  
H. SAMEA
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Segal Algebra ◽  
Amenable Banach Algebra ◽  
Segal Algebras

AbstractA number of well-known results of Ghahramani and Loy on the essential amenability of Banach algebras are generalized. It is proved that a symmetric abstract Segal algebra with respect to an amenable Banach algebra is essentially amenable. Applications to locally compact groups are given.

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.

On amenability of the Banach algebras l∞(S, [Ufr ])

2002 ◽  
Vol 132 (2) ◽  
pp. 319-322
Author(s):  
FÉLIX CABELLO SÁNCHEZ ◽  
RICARDO GARCÍA
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Short Note ◽  
Basic Information ◽  
Arens Product ◽  
Pointwise Multiplication ◽  
Weak Amenability ◽  
Usual Norm ◽  
Bounded Functions ◽  
Second Dual

Let [Ufr ] be an associative Banach algebra. Given a set S, we write l∞(S, [Ufr ]) for the Banach algebra of all bounded functions f: S→[Ufr ] with the usual norm ∥f∥∞ = sups∈S∥f(s)∥[Ufr ] and pointwise multiplication. When S is countable, we simply write l∈([Ufr ]).In this short note, we exhibit examples of amenable (resp. weakly amenable) Banach algebras [Ufr ] for which l∈(S, [Ufr ]) fails to be amenable (resp. weakly amenable), thus solving a problem raised by Gourdeau in [7] and [8]. We refer the reader to [4, 9, 10] for background on amenability and weak amenability. For basic information about the Arens product in the second dual of a Banach algebra the reader can consult [5, 6].

Weak module amenability of triangular Banach algebras

2011 ◽  
Vol 61 (6) ◽  
Author(s):  
Abdolrasoul Pourabbas ◽  
Ebrahim Nasrabadi
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Module Amenability ◽  
Weak Amenability ◽  
Weak Module ◽  
Triangular Banach Algebras

AbstractLet A and B be unital Banach algebras and let M be a unital Banach A,B-module. Forrest and Marcoux [6] have studied the weak amenability of triangular Banach algebra $\mathcal{T} = \left[ {_B^{AM} } \right]$ and showed that T is weakly amenable if and only if the corner algebras A and B are weakly amenable. When $\mathfrak{A}$ is a Banach algebra and A and B are Banach $\mathfrak{A}$-module with compatible actions, and M is a commutative left Banach $\mathfrak{A}$-A-module and right Banach $\mathfrak{A}$-B-module, we show that A and B are weakly $\mathfrak{A}$-module amenable if and only if triangular Banach algebra T is weakly $\mathfrak{T}$-module amenable, where $\mathfrak{T}: = \{ [^\alpha _\alpha ]:\alpha \in \mathfrak{A}\} $.

scholarly journals Approximate complementation and its applications in studying ideals of Banach algebras

2003 ◽  
Vol 92 (2) ◽  
pp. 301 ◽  
Author(s):  
Yong Zhang
Keyword(s):  
Banach Space ◽  
Banach Algebra ◽  
Compact Subset ◽  
Approximation Property ◽  
Banach Algebras ◽  
Approximate Identity ◽  
Amenable Banach Algebra

We show that a subspace of a Banach space having the approximation property inherits this property if and only if it is approximately complemented in the space. For an amenable Banach algebra a closed left, right or two-sided ideal admits a bounded right, left or two-sided approximate identity if and only if it is bounded approximately complemented in the algebra. If an amenable Banach algebra has a symmetric diagonal, then a closed left (right) ideal $J$ has a right (resp. left) approximate identity $(p_{\alpha})$ such that, for every compact subset $K$ of $J$, the net $(a\cdot p_{\alpha})$ (resp. $(p_{\alpha}\cdot a)$) converges to $a$ uniformly for $a \in K$ if and only if $J$ is approximately complemented in the algebra.

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