Bornological projective limits of inductive limits of normed spaces

TL;DR

This paper provides a criterion to determine when certain complex topological vector spaces, formed by limits of normed spaces, are bornological, linking abstract homological conditions with functional analysis.

Contribution

It introduces a new criterion for bornologicity of projective limits of inductive limits of normed spaces, connecting homological algebra and functional analysis conditions.

Findings

Established a criterion for bornological projective limits.

Compared the criterion with known homological algebra conditions.

Linked conditions to weighted PLB-spaces of continuous functions.

Abstract

We establish a criterion to decide when a countable projective limit of countable inductive limits of normed spaces is bornological. We compare the conditions occurring within our criterion with well-known abstract conditions from the context of homological algebra and with conditions arising within the investigation of weighted PLB-spaces of continuous functions.