Banach algebras and analytic functions

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...

Non-reflexivity of the Derivation Space from Banach Algebras of Analytic Functions

Let Ω be an open connected subset of the plane, and let A be a Banach algebra of analytic functions on Ω. We show that the space of bounded derivations from A into A∗ is not reflexive. We also obtain similar results when A = C(n)[0, 1] for n ≥ 2.

Spectra of Composition Operators on Algebras of Analytic Functions on Banach Spaces

Let E be a Banach space, with unit ball BE . We study the spectrum and the essential spectrum of a composition operator on H∞(BE) determined by an analytic symbol with a fixed point in BE . We relate the spectrum of the composition operator to that of the derivative of the symbol at the fixed point. We extend a theorem of Zheng to the context of analytic symbols on the open unit ball of a Hilbe...

Biflatness and Biprojectivitiy of Triangular Banach Algebras

The Exponential and Logarithmic Functions on Commutative Banach Algebras

In this paper we define the two important functions exp and log on a commutative Banach algebra B with unit e. Some important properties of these functions are established. The proofs given here have elementary character.