On the structure of rank one elements in Banach algebras.
On the weak amenability of ℬ(X)
We investigate the weak amenability of the Banach algebra ℬ(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.
On topological algebras
On Α Bochner΄s Type Theorem in Topological Algebras
Operator Connes-amenability of completely bounded multiplier Banach algebras
For a completely contractive Banach algebra , we find conditions under which the completely bounded multiplier algebra is a dual Banach algebra and the operator amenability of is equivalent to the operator Connes-amenability of . We also show that, in this case, these are equivalent to the existence of a normal virtual operator diagonal.
Point derivations on the L¹-algebra of polynomial hypergroups
We investigate whether the L¹-algebra of polynomial hypergroups has non-zero bounded point derivations. We show that the existence of such point derivations heavily depends on growth properties of the Haar weights. Many examples are studied in detail. We can thus demonstrate that the L¹-algebras of hypergroups have properties (connected with amenability) that are very different from those of groups.
Polynomial identification in uniform and operator algebras.
Polynomially compact derivations on Banach algebras
We consider a continuous derivation D on a Banach algebra 𝓐 such that p(D) is a compact operator for some polynomial p. It is shown that either 𝓐 has a nonzero finite-dimensional ideal not contained in the radical rad(𝓐) of 𝓐 or there exists another polynomial p̃ such that p̃(D) maps 𝓐 into rad(𝓐). A special case where Dⁿ is compact is discussed in greater detail.
Problems concerning -weak amenability of a Banach algebra
In this paper we extend the notion of -weak amenability of a Banach algebra when . Technical calculations show that when is Arens regular or an ideal in , then is an -module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of -weak amenability to .
Propriétés analytiques du spèctre dans les algèbres de Jordan-Banach.
Pseudo-amenability of Brandt semigroup algebras
In this paper it is shown that for a Brandt semigroup over a group with an arbitrary index set , if is amenable, then the Banach semigroup algebra is pseudo-amenable.
Real Gelfand-Mazur algebras.
Real Gel'fand-Mazur division algebras.
Remarks on Segal Algebras.
Renormalizations of Banach and locally convex algebras
Representation of locally convex algebras.
We deal with the representation of locally convex algebras. On one hand as subalgebras of some weighted space CV(X) and on the other hand, in the case of uniformly A-convex algebras, as inductive limits of Banach algebras. We also study some questions on the spectrum of a locally convex algebra.
Representations of topological algebras by projective limits.
Semi-simplicity of a proper weak -algebra.
Short Proofs of Some Structure Theorems on m-Convex Algebras
Solved and unsolved problems in generalized notions of amenability for Banach algebras
We survey the recent investigations on approximate amenability/contractibility and pseudo-amenability/contractibility for Banach algebras. We will discuss the core problems concerning these notions and address the significance of any solutions to them to the development of the field. A few new results are also included.