Projective limits of weighted LB-spaces of holomorphic functions

TL;DR

This paper extends the study of PLB-spaces from continuous functions to holomorphic functions, analyzing their properties and the conditions for limit interchangeability based on weight sequences.

Contribution

It introduces a comprehensive analysis of projective limits of weighted spaces of holomorphic functions, expanding prior work on continuous functions.

Findings

Characterization of locally convex properties via weight sequences

Conditions for interchangeability of projective and inductive limits

Extension of PLB-space theory to holomorphic functions

Abstract

Countable projective limits of countable inductive limits, called PLB-spaces, of weighted Banach spaces of continuous functions have recently been investigated by Agethen, Bierstedt and Bonet. We extend their investigation to the case of holomorphic functions regarding the same type of questions, i.e. we analyze locally convex properties in terms of the defining double sequence of weights and study the interchangeability of projective and inductive limit.