On the transformation of vector-valued sequences by linear and multilinear operators

In this paper we provide an abstract aproach to the study of classes of multiple summing multilinear operators between Banach spaces. The main purpose is unify the study of several known classes and results, for example multiple (p, q 1 , . . . , q n )summing operators, multiple mixing (s, q, p)-summing operators and multiple strong (s, q, p)-mixing summing operators. We also define new class of multiple summing multilinear operator that are particular cases of our construction and, therefore, satisfy the results proved in the paper. * joilsonor@ufba.br † Supported by CAPES doctoral scholarship. 2010 Mathematics Subject Classification: 46B45, 47L22, 40Bxx.

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“…Note that the concept of n-sequence class generalizes the concept of sequence class introduced in the literature by Botelho and Campos in [6].…”

Section: Introductionmentioning

confidence: 91%

“…where e j is the vector with 1 in the j-th coordinate and zero in the other coordinates, and the symbol E 1 ֒→ F means that E is a linear subspace of F and x F ≤ x E . Still according to [6], the sequence class γ s is said to be:…”

Section: Introductionmentioning

confidence: 99%

Generalized Multiple Summing Multilinear Operators on Banach Spaces

Ribeiro

Santos

2019

Mediterr. J. Math.

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“…A usual approach, proving all the desired properties using the definitions of the underlying sequence spaces, would lead to long and boring proofs. Alternatively, we shall apply the abstract framework constructed in [3] to deal with this kind of operators. In this fashion we will end up with short and concise proofs.…”

Section: The Space ℓ Mid P (E)mentioning

confidence: 99%

“…Instead of its definition, we shall use that the class of mid p-summable sequences enjoys the two properties we prove below. For the definitions of finitely determined and linearly stable sequence classes, see [3].…”

Section: The Space ℓ Mid P (E)mentioning

confidence: 99%

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Operator ideals related to absolutely summing and Cohen strongly summing operators

2017

Self Cite

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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.

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Tensor Characterizations of Summing Polynomials

et al. 2018

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Operators T that belong to some summing operator ideal, can be characterized by means of the continuity of an associated tensor operator T that is defined between tensor products of sequences spaces. In this paper we provide a unifying treatment of these tensor product characterizations of summing operators. We work in the more general frame provided by homogeneous polynomials, where an associated "tensor" polynomial-which plays the role of T-, needs to be determined first. Examples of applications are shown.

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On the transformation of vector-valued sequences by linear and multilinear operators

Cited by 31 publications

References 34 publications

Generalized Multiple Summing Multilinear Operators on Banach Spaces

Generalized Multiple Summing Multilinear Operators on Banach Spaces

Operator ideals related to absolutely summing and Cohen strongly summing operators

Tensor Characterizations of Summing Polynomials

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