A few remarks on bounded operators on topological vector spaces

TL;DR

This paper explores various bounded operators on topological vector spaces, their relation to compact operators, and extends the discussion to bilinear mappings, tensor products, and operators on Riesz spaces.

Contribution

It provides new insights into the conditions under which bounded operators coincide with compact operators and examines their properties in different topological vector space contexts.

Findings

Identifies conditions where bounded and compact operators coincide.

Analyzes properties of tensor product operators in locally convex spaces.

Studies operators on topological Riesz spaces.

Abstract

We give a few observations on different types of bounded operators on a topological vector space X and their relations with compact operators on X. In particular, we investigate when these bounded operators coincide with compact operators. We also consider similar types of bounded bilinear mappings between topological vector spaces. Some properties of tensor product operators between locally convex spaces are established. In the last part of the paper we deal with operators on topological Riesz spaces.