SOME RESULTS ON SEMI-REFLEXIVITY AND REFLEXIVITY IN LOCALLY CONVEX SPACES

Abstract

In this paper we discuss that if E[] is a barreled space such that every bounded subset of E is relatively compact, then E[] is reflexive, and that a barreled space E[τ] in which there is a denumerable system of convex compact subsets is reflexive. We also discuss Some hereditary-type properties of reflexive locally convex spaces.

Keywords: Bornological space, barreled, hereditarily-reflexive, M-space, quasi-complete, reflexive, strong dual.

AMS (2010) Mathematics Subject Classification: 46A25.