Lineability of the set of bounded linear non-absolutely summing operators

TL;DR

This paper investigates the lineability of the set of bounded linear operators that are not absolutely summing, providing solutions to a previously posed question and extending the approach to related contexts.

Contribution

It offers a nearly complete answer to the lineability question for bounded non-absolutely summing operators and introduces adaptable proof techniques.

Findings

The set of bounded non-absolutely summing operators is lineable in most cases.

The proof method can be adapted to other operator classes.

The question remains open only for extremely pathological cases.

Abstract

In this note we solve, except for extremely pathological cases, a question posed by Puglisi and Seoane-Sepulveda on the lineability of the set of bounded non-absolutely summing linear operators. We also show how the idea of the proof can be adapted to several related situations.