On certain quasi-complemented and complemented Banach algebras.
On character amenable Banach algebras
We obtain characterizations of left character amenable Banach algebras in terms of the existence of left ϕ-approximate diagonals and left ϕ-virtual diagonals. We introduce the left character amenability constant and find this constant for some Banach algebras. For all locally compact groups G, we show that the Fourier-Stieltjes algebra B(G) is C-character amenable with C < 2 if and only if G is compact. We prove that if A is a character amenable, reflexive, commutative Banach algebra, then A...
On circle-Exponential Topological Algebras
On Cohen's proof of the Factorization Theorem
Various proofs of the Factorization Theorem for representations of Banach algebras are compared with its original proof due to P. Cohen.
On (Co)homology of triangular Banach algebras
Suppose that A and B are unital Banach algebras with units and , respectively, M is a unital Banach A,B-module, is the triangular Banach algebra, X is a unital -bimodule, , , and . Applying two nice long exact sequences related to A, B, , X, , , and we establish some results on (co)homology of triangular Banach algebras.
On Continuity of Algebra Homomorphisms and Uniqueness of Metric Topology.
On derivations and crossed homomorphisms
We discuss some results about derivations and crossed homomorphisms arising in the context of locally compact groups and their group algebras, in particular, L¹(G), the von Neumann algebra VN(G) and actions of G on related algebras. We answer a question of Dales, Ghahramani, Grønbæk, showing that L¹(G) is always permanently weakly amenable. Then we show that for some classes of groups (e.g. IN-groups) the homology of L¹(G) with coefficients in VN(G) is trivial. But this is no longer true, in general,...
On differences of Riesz homomorphisms.
On discontinuity of the spectral radius in Banach algebras
On domination problem in Banach algebras
On functional representation of locally -pseudoconvex algebras.
On Gelfand-Mazur theorem on a class of F -algebras
A topological algebra A is said to be fundamental if there exists b > 1 such that for every sequence (xn) in A, (xn) is Cauchy whenever the sequence bn(xn − xn-1) tends to zero as n → ∞. Let A be a complex unital fundamental F-algebra with bounded elements such that A* separates the points on A. Then we prove that the spectrum σ(a) of every element a ∈ A is nonempty compact. Moreover, if A is a division algebra, then A is isomorphic to the complex numbers ℂ. This result is a generalization of...
On generalized right modular complemented algebras
On generalized topological divisors of zero
On holomorphy in Banach spaces and absolute convergence of Fourier series
On inductive limits of topological algebras
On innerness of derivations on .
On inverse-closed algebras of infinitely differentiable functions
On JB*-triples defined by fibre bundles.
On joint spectra of operators on a Banach space isomorphic to its square