Weak Cone-Completeness of Direct Sums in Locally Convex Cones

Year 2019, Volume: 1 Issue: 1, 11 - 15, 15.06.2019

Mohammad Reza Motallebi

Abstract

We consider the weak cone-completeness in locally convex cones and prove that the direct sum of a family of weakly cone-complete separated locally convex cones is weakly cone-complete. We conclude that a direct sum cone topology is barreled whenever its components are weakly cone-complete and separated with the countable bases.

Keywords

Locally convex cones, direct sums, weak cone-completeness

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