Operator ideals related to absolutely summing and Cohen strongly summing operators

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 [12] 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.

Injective Polynomial Ideals and The Domination Property

“…Since I P−dual = I dual • P for every operator ideal I [5, Theorem 2.2], the result follows from Corollary 3.6. Now we characterize the polynomial duals of the ideal K p of p-compact operators (see [20]) and of the ideal D p of Cohen strongly p-summing operators (see [4,9]). N p stands for the ideal of p-nuclear operators and I p for the ideal of p-integral operators (see [18]).…”

Tensor Characterizations of Summing Polynomials

“…Several classes of linear operators that relate weakly/absolutely/strongly summable sequences have been extensively treated in the literature (e.g. [8,16,17,23]).…”

Espaços de sequências vetoriais e ideais de operadores

“…Além de resgatar muitos ideais que vinham sendo estudados separadamente, esta abordagem abstrata permite que novos ideais, que assim possam ser caracterizados, que venham a ser introduzidos no futuro já tenham sua teoria básica estabelecida. Por sinal,é isso exatamente o que aconteceu com os novos ideais de operadores estudados por Botelho, Campos e Santos [5].…”