Directed Banach spaces of affine functions

Holomorphic functions on Banach spaces

This is a survey about some problems from the theory of holomorphic functions on Banach spaces which have attracted the attention of many researchers during the last thirty years.

Convergence of an Implicit Iteration for Affine Mappings in Normed and Banach Spaces

Banach and Fréchet spaces of functions

Many familiar and useful spaces of continuous or differentiable functions are Hilbert or Banach spaces, with pleasant completeness properties, but many are not. Some are Fréchet spaces, thus still complete, but lacking some of the conveniences of Banach spaces. Some other important spaces are not Fréchet, either. Still, some of these important spaces are colimits of Fréchet spaces (or of Banach...

Rigidity of Commuting Affine Actions on Reflexive Banach Spaces

We give a simple argument to show that if α is an affine isometric action of a product G ×H of topological groups on a reflexive Banach space X with linear part π, then either π(H) fixes a unit vector or α|G almost fixes a point on X . It follows that if π is an isometric linear representation of a topological group G on a reflexive space X such that π(Z(G)) has no fixed unit vectors, then the ...

Mean Periodic Functions in Banach Spaces

Here we give a necessary and sufficient condition for a Banach space to be separable.