Equicontinuity and Bilinear Mappings

Interconnections between boundedness and equicontinuity in bilinear mappings

Abstract

We consider various types of boundedness, equicontinuity and sequential equicontinuity for sets of separately continuous bilinear mappings between topological modules. Our purpose here is to establish relations among the various notions of boundedness (resp. equicontinuity, sequential equicontinuity) under consideration, as well as to establish relations among notions of a different nature for example, to obtain conditions under which point wise boundedness implies separate equicontinuity.