Bounded linear mappings of finite rank

Abstract

This paper comprises a constructive investigation of the relationship between compactness, finite rank and located kernel for a bounded linear mapping into a finite-dimensional normed space. The main result is that a bounded linear mapping of a normed space into a finite-dimensional normed space is constructively compact if and only if its kernel is located. Several examples are given which highlight the constructive distinction between a mapping into a finite-dimensional space and a mapping with finite-dimensional range.