Banach algebras of weakly differentiable functions

Compact endomorphisms of Banach algebras of infinitely differentiable functions

Let (Mn) be a sequence of positive numbers satisfying M0 = 1 and Mn+m MnMm ≥ ( n+m n ) , m, n, non-negative integers. We let D([0, 1],M) = {f ∈ C∞([0, 1]) : ‖f‖ = ∞ ∑

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...

Endomorphisms of Banach algebras of infinitely differentiable functions on compact plane sets

This note is a sequel to [7] where we investigated the endomorphisms of a certain class of Banach algebras of infinitely differentiable functions on the unit interval. Start with a perfect, compact plane setX. We say that a complex-valued function f defined on X is complex-differentiable at a point a ∈ X if the limit f (a) = lim z→a, z∈X f(z)− f(a) z − a exists. We call f ′(a) the complex deriv...

Completions of normed algebras of differentiable functions

In this paper we look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions considered by Dales and Davie in [7]. For many compact plane sets the classical definitions give rise to incomplete spaces. We introduce an alternative definition of differentiability which allows us to describe the completions of these spaces. We...

On distribution functions of the derivatives of weakly differentiable mappings