Operator ideals related to absolutely summing and Cohen strongly summing operators

Geraldo Botelho, Jamilson R. Campos and Joedson Santos

Vol. 287 (2017), No. 1, 1–17

DOI: 10.2140/pjm.2017.287.1

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 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 nonabsolutely summing operators is given.

Keywords

Banach sequence spaces, operator ideals, summing operators.

Mathematical Subject Classification 2010

Primary: 46B45

Secondary: 47B10, 47L20

Milestones

Received: 6 February 2016

Accepted: 4 August 2016

Published: 6 February 2017