A remark on condensation of singularities

TL;DR

This paper presents a simplified proof of a stronger condensation of singularities principle for non-linear operators on quasi-Banach spaces, extending previous results and demonstrating the technique's versatility.

Contribution

It introduces a concise, elementary proof of a generalized condensation of singularities principle using techniques similar to Sokal's proof of the uniform boundedness principle.

Findings

Simplified proof of the condensation of singularities principle

Extension to certain non-linear operators on quasi-Banach spaces

Generalization beyond previous results of Gál

Abstract

Recently Alan D. Sokal gave a very short and completely elementary proof of the uniform boundedness principle. The aim of this note is to point out that by using a similiar technique one can give a considerably short and simple proof of a stronger statement, namely a principle of condensation of singularities for certain double-sequences of non-linear operators on quasi-Banach spaces, which is a bit more general than a result of I.\,S. G\'al.