Maximal ideals of generalized summing linear operators

TL;DR

This paper characterizes when certain Banach ideals of linear operators, defined via vector-valued sequences, are maximal, using tensor quasi-norms and duality theory, extending known results and providing new insights.

Contribution

It establishes criteria for maximality of Banach ideals of sequence-based operators and develops duality theory for associated tensor quasi-norms, generalizing previous results.

Findings

Identifies conditions for maximality of sequence-based operator ideals

Develops duality theory for tensor quasi-norms

Extends known results and introduces new characterizations

Abstract

We prove when a Banach ideal of linear operators defined, or characterized, by the transformation of vector-valued sequences is maximal. Known results are recovered as particular cases and new information is obtained. To accomplish this task we study a tensor quasi-norm determined by the underlying sequence classes. The duality theory for these tensor quasi-norms is also developed.