Density theorems for algebras of operators and annihilator Banach algebras.

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...

Linear operators of Banach spaces with range in Lipschitz algebras

In this paper, a complete description concerning linear operators of Banach spaces with range in Lipschitz algebras $lip_al(X)$ is provided. Necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. Finally, a lower bound for the essential norm of such operators is obtained.

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

Multiplication operators on Banach modules over spectrally separable algebras

‎Let $mathcal{A}$ be a commutative Banach algebra and $mathscr{X}$ be a left Banach $mathcal{A}$-module‎. ‎We study the set‎ ‎${rm Dec}_{mathcal{A}}(mathscr{X})$ of all elements in $mathcal{A}$ which induce a decomposable multiplication operator on $mathscr{X}$‎. ‎In the case $mathscr{X}=mathcal{A}$‎, ‎${rm Dec}_{mathcal{A}}(mathcal{A})$ is the well-known Apostol algebra of $mathcal{A}$‎. ‎We s...

Biflatness and Biprojectivitiy of Triangular Banach Algebras