A Minimax Lemma and its Applications

TL;DR

This paper presents a simplified version of the minimax theorem without topological assumptions, leading to new domination criteria and applications to p-summing operators.

Contribution

It introduces an easy, assumption-free minimax lemma and demonstrates its utility in deriving domination criteria and applications in operator theory.

Findings

Established a topologically assumption-free minimax lemma

Derived new domination criteria from the lemma

Applied the lemma to p-summing operators

Abstract

We prove an easy version of the minimax theorem with no topological assumption. We deduce from it some domination criteria as well as an application to $p$-summing operators.