Operator ideals related to absolutely summing and Cohen strongly summing operators

TL;DR

This paper investigates operator ideals linked to summing operators and introduces new sequence spaces, providing new factorization theorems and insights into the structure of non-absolutely summing operators.

Contribution

It introduces a new sequence space and explores its connection to classical summing operator ideals, offering new factorization results and structural insights.

Findings

Proves a new factorization theorem for absolutely summing operators.

Contributes to understanding the existence of infinite-dimensional spaces of non-absolutely summing operators.

Analyzes operator ideals related to a new sequence space introduced by Karn and Sinha.

Abstract

We study the ideals of linear operators between Banach spaces determined by the transformation of vector-valued sequences involving the new sequence space introduced by Karn and Sinha \cite{karnsinha} and the classical spaces of absolutely, weakly and Cohen strongly summable sequences. As applications, we prove a new factorization theorem for absolutely summing operators and a contribution to the existence of infinite dimensional spaces formed by non-absolutely summing operators is given.