Related papers: A Connes-amenable, dual Banach algebra need not ha…

Recent developments in Banach space theory provided unexpected examples of unital Banach algebras that are isomorphic to Calkin algebras of Banach spaces, however no example of a unital Banach algebra that cannot be realised as a~Calkin…

In this note the result by A. Swift concerning the embeddability of countably branching bundle graphs into Banach spaces is extended from the context of reflexive spaces with an unconditional asymptotic structure to the context of dual…

We prove that, if a discrete group $G$ is not inner amenable, then the unit group of the ring of operators affiliated with the group von Neumann algebra of $G$ is non-amenable with respect to the topology generated by its rank metric. This…

We let the central Fourier algebra, ZA(G), be the subalgebra of functions u in the Fourier algebra A(G) of a compact group, for which u(xyx^{-1})=u(y) for all x,y in G. We show that this algebra admits bounded point derivations whenever G…

In 1972, the late B. E. Johnson introduced the notion of an amenable Banach algebra and asked whether the Banach algebra $B(E)$ of all bounded linear operators on a Banach space $E$ could ever be amenable if $\dim E = \infty$. Somewhat…

For a locally compact group $G$, let $A(G)$ denote its Fourier algebra, $M_{cb}(A(G))$ the completely bounded multipliers of $A(G)$, and $A_{M_cb}(G)$ the closure of $A(G)$ in $M_{cb}(A(G))$. We show that, if $A_{M_cb}(G)$ is amenable, then…

The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem~2 which states that for a locally compact group $G$, $G$ is compact if there…

In this paper we introduce (weakly) root graded Banach--Lie algebras and corresponding Lie groups as natural generalizations of group like $\GL_n(A)$ for a Banach algebra $A$ or groups like $C(X,K)$ of continuous maps of a compact space $X$…

It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C$^*$-algebra. This implies that the weakly almost periodic functionals on $M(G)$, the measure…

To each 2-dimensional irreducible p-adic representation of Gal(Qpbar/Qp) which becomes crystalline over an abelian extension of Q_p, we associate a Banach space B(V) endowed with a linear continuous unitary action of GL_2(Q_p). When V is…

A topological group $G$ is called extremely amenable if every continuous action of $G$ on a compact space has a fixed point. This concept is linked with geometry of high dimensions (concentration of measure). We show that a von Neumann…

Let $S$ be an inverse semigroup with the set of idempotents $E$. In this paper we define the module super-amenability of a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and show that when $E$…

Let G be a locally compact abelian group, $\omega:G\to (0,\infty)$ be a weight, and ($\Phi$,$\Psi$) be a complementary pair of strictly increasing continuous Young functions. We show that for the weighted Orlicz algebra $L^\Phi_\omega(G)$,…

For every Banach space $X$ with a Schauder basis consider the Banach algebra $\mathbb{R} I\oplus\mathcal{K}_\mathrm{diag}(X)$ of all diagonal operators that are of the form $\lambda I + K$. We prove that $\mathbb{R}…

We show that every infinite-dimensional Banach space with separable dual admits an equivalent norm which is weakly locally uniformly rotund but not locally uniformly rotund.

We provide a characterization of the Banach spaces $X$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ which have the property that the dual space $X^*$ is naturally isomorphic to the space $\mathcal{L}_{diag}(X)$ of diagonal operators with…

We give an affirmative answer to a question due to M. Megrelishvili, and show that for every locally compact group $G$ we have $\operatorname{Tame}(L^{1}(G)) = \operatorname{Tame}(G)$, which means that a functional is tame over $L^{1}(G)$…

For appropriate parameters $k,p,q$, we introduce and systematically study the class of $(k,p,q)$-differential subalgebras. This is a vast class of Banach $^*$-algebras defined by their relation with their $C^*$-envelopes. Some examples are…

This paper will generalize what may be termed the "geometric duality theory" of real pre-ordered Banach spaces which relates geometric properties of a closed cone in a real Banach space, to geometric properties of the dual cone in the dual…

Let $G$ be a locally compact Abelian group, and $w: G\to (0, \infty)$ be a Borel measurable weighted function. In this paper, the algebraic and topological properties of group algebra are studied and assessed. We show that the weighted…