Vol. 287, No. 1, 2017

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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
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