Metrizability of spaces of homomorphisms between metric vector spaces

TL;DR

This paper investigates conditions under which spaces of continuous linear maps between metric vector spaces are metrizable, aiming to identify a class of metric vector spaces with this property.

Contribution

It provides insights into the metrizability of large spaces of linear maps, contributing to the understanding of the structure of function spaces in metric vector spaces.

Findings

Identifies conditions for metrizability of spaces of linear maps

Characterizes classes of metric vector spaces with metrizable homomorphism spaces

Advances understanding of topological properties of function spaces

Abstract

This note tries to give an answer to the following question: Is there a sufficiently rich class of metric vector spaces such that sufficiently large spaces of continuous linear maps between them are metrizable?