Related papers: (Non-)amenability of B(E)

Let $T$ be a Banach algebra homomorphism from a Banach algebra $\mathcal B$ to a Banach algebra $\mathcal A$ with $\|T\|\leq 1$. Recently it has been obtained some results about Arens regularity and also various notions of amenability of…

We prove that the crossed product Banach algebra $\ell^1(G,A;\alpha)$ that is associated with a ${\mathrm C}^\ast$-dynamical system $(A,G,\alpha)$ is amenable if $G$ is a discrete amenable group and $A$ is a strongly amenable ${\mathrm…

We present some extensions of classical results that involve elements of the dual of Banach spaces, such as Bishop-Phelp's theorem and James' compactness theorem, but restricting to sets of functionals determined by geometrical properties.…

Runde and Spronk showed in 2004 that there are non-amenable groups $G$, including $\mathbb F_2$, {whose Fourier-Stieltjes algebra, $B(G)$,} is operator Connes-amenable. This result was surprising since the measure algebra $M(G)$ is…

In this paper we deal with four generalized notions of amenability which are called approximate, approximate weak, approximate cyclic and approximate $n$-weak amenability. The first two were introduced and studied by Ghahramani and Loy in…

In this paper, we introduce and investigate the concepts of cyclically weakly amenable and point amenable. Then, we compare these concepts with the concepts of weakly amenable and cyclically amenable and find the relation between them. For…

For every $ 1 < p < \infty $ an isomorphically polyhedral Banach space $E_p$ is constructed having an unconditional basis and admitting a quotient isomorphic to $\ell_p$. It is also shown that $E_p$ is not isomorphic to a subspace of a…

Assuming the generalized continuum hypothesis we construct arbitrarily big indecomposable Banach spaces. i.e., such that whenever they are decomposed as $X\oplus Y$, then one of the closed subspaces $X$ or $Y$ must be finite dimensional. It…

Let $X$ be a compact Hausdorff space and $A$ a Banach algebra. We investigate amenability properties of the algebra $C(X,A)$ of all $A$-valued continuous functions. We show that $C(X,A)$ has a bounded approximate diagonal if and only if $A$…

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)…

Given a Boolean algebra $A$, we construct another Boolean algebra $B$ with no uncountable well-ordered chains such that the Banach space of real valued continuous functions $C(K_A)$ embeds isometrically into $C(K_B)$, where $K_A$ and $K_B$…

In this paper we study unimodular amenable groups. The first part is devoted to results on the existence of uniform families of epsilon-quasi tilings for these groups. In this context, constructions of Ornstein and Weiss are extended by…

There has been a long-standing conjecture in Banach algebra that every amenable operator is similar to a normal operator. In this paper, we study the structure of amenable operators on Hilbert spaces. At first, we show that the conjecture…

The following theorem is the main result of this note. Theorem 1. Let $(E, \|\cdot\|_E) $ be a rearrangement invariant Banach function space on the interval $[0, 1]$. If $E$ is isometric to $\L_p [0, 1]$ for some $1\le p<\infty$, then $E$…

Motivated by a seminal paper of professor M. Z. Nashed published in 1987 on classification of ill-posed linear operator equations and distinguishing two types of ill-posedness in Banach and Hilbert spaces, we present, illustrate and justify…

Let $G$ be a locally compact abelian group, and let $\omega:G \to [1,\infty)$ be a measurable weight, i.e., $\omega$ is measurable, and $\omega(s+t)\leq \omega(s)\omega(t)$ for all $s, t \in G$. Let $\mathcal{A}$ be a semisimple commutative…

Let $\mathcal A$ be a Banach algebra. Using the concept of module biflatness, we show that the module amenability of the second dual $\mathcal A^{**}$ (with the first Arens product) necessitates the module amenability of $\mathcal A$. We…

The ``multiple of the inclusion plus compact problem'' which was posed by T.W. Gowers in 1996 and Th. Schlumprecht in 2003, asks whether for every infinite dimensional Banach space $X$ there exists a closed subspace $Y$ of $X$ and a bounded…

In this paper, we study the hereditary properties of module $(\phi,\varphi)$-amenability on Banach algebras. We also define the concept of module character contractibility for Banach algebras and obtain characterizations of module character…

The classical Banach--Mazur theorem asserts that every separable Banach space admits an isometric embedding into $C[0,1]$. It is also well known that every separable Banach space embeds isometrically into $\ell^\infty$. We show that such an…