Some special operators and new classes of locally convex spaces

Abstract

We consider some special operators on a locally convex Hausdorff space to itself, which have neat spectral theories and prove some perturbation results. This leads us to define and study a few special classes of locally convex spaces in which various subsets of the algebra of continuous linear operators either coincide or are closely related with each other. These are then compared to the classes of barrelled, infrabarrelled and DF-spaces and examples are given to distinguish them from one another.

Boundedness and completeness in locally convex spaces and algerbras

“…The following class of operators was first defined in Appendix A of Michael (1952); they appear also in Moore (1968) and Chilana (1972) and numerical range theory for operators of this class was studied in Giles, Joseph, Koehler and Sims (1975). DEFINITION 3.3.…”