Related papers: A simple proof of a theorem on (2n)-weak amenabili…

We investigate weak amenability of the Banach algebra A(X) of approximable operators on a Banach space X and its relation to factorization properties of operators in A(X). We show that if A(X) is weakly amenable, then either A(X) is…

In this note, we study the Arens regularity of projective tensor product $A\hat{\otimes}B$ whenever $A$ and $B$ are Arens regular. We establish some new conditions for showing that the Banach algebras $A$ and $B$ are Arens regular if and…

For a topological group $G$, amenability can be characterized by the amenability of the convolution Banach algebra $L^1(G)$. Here a Banach algebra $A$ is called amenable if every bounded derivation from $A$ into any dual--type…

In this paper we prove that if (A,\pi) is an amenable Banach algebra and if \rho is another Banach algebra multiplication on A such that the difference between \rho and and \pi is less than 1/11, then (A, \rho) is also amenable.

We show that the tensor product of approximately amenable algebras need not be approximately amenable, and investigate conditions under which $A$ and $B$ being approximately amenable implies, or is implied by, $A\hat{\otimes}B$ or…

Let G be a compact connected Lie group. We prove that the Fourier algebra A(G) is weakly amenable if and only if G is abelian.

In this paper, we introduce and study some notations of amenability such as $n$-ideal amenability and $n$-weak amenability for Frechet algebra and we examine how these concepts in Banach algebra can be generalized and defined for Frechet…

We investigate the notions of amenability and its related homological notions for a class of $I\times I$-upper triangular matrix algebra, say $UP(I,A)$, where $A$ is a Banach algebra equipped with a non-zero character. We show that…

We show that if $T$ is an isometry (as metric spaces) between the invertible groups of unital Banach algebras, then $T$ is extended to a surjective real-linear isometry up to translation between the two Banach algebras. Furthermore if the…

In this paper, we introduce the concept of biamenability of Banach algebras and we show that despite the apparent similarities between amenability and biamenability of Banach algebras, they lead to very different, and somewhat opposed,…

We investigate whether almost weak stability of an operator $T$ on a Banach space $X$ implies its almost weak polynomial stability. We show, using a modified version of the van der Corput Lemma that if $X$ is a Hilbert space and $T$ a…

Our main result is the following: {\it Let $E$ be a Banach space and $D$ be a weakly compact subset of $E$ with $0\notin D$. If $A$ is a bounded subset of $E$ such that every $x^*\in E^*$ with $x^*(D) >0$ attains its supremum on $A$, then…

It is shown that the dual $\hat{A}$ of a separable $C^{\ast}$-algebra $A$ is discrete if and only if its Banach space dual has the weak$^{\ast}$-fixed point property. We prove further that these properties are equivalent to the uniform…

We show that if $T$ is an isometry (as metric spaces) from an open subgroup of the group of the invertible elements in a unital semisimple commutative Banach algebra onto an open subgroup of the group of the invertible elements in a unital…

We show that an \'etale groupoid which is strongly amenable at infinity is amenable whenever its full and reduced $C^*$-algebras coincide.

Let $X$ and $Y$ be separable Banach spaces. Suppose $Y$ either has a shrinking basis or $Y$ is isomorphic to $C(2^\mathbb{N})$ and $A$ is a subset of weakly compact operators from $X$ to $Y$ which is analytic in the strong operator…

We show that, given a Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded)…

For a monic polynomial p(z) with coefficients in a unital complex Banach algebra, we prove that there exist a complex number z such that p(z)is not invertible

In this paper, we study the notion of approximately bi at Banach algebras for second dual Banach algebras and semigroup algebras. We show that for a locally compact group G, if S(G)?? is approximately bi at, then G is amenable group. Also…

In this paper, we study the notion of Connes amenability for a class of $I\times{I}$-upper triangular matrix algebra $UP(I,\mathcal{A})$, where $\mathcal{A}$ is a dual Banach algebra with a non-zero $wk^\ast$-continuous character and $I$ is…