An anisotropic summability and mixed sequences

Jamilson R. Campos; Renato Macedo; Joedson Santos

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arXiv · 2204.08313

An anisotropic summability and mixed sequences

Jamilson R. Campos·Renato Macedo·Joedson Santos

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Abstract

In this paper we define and study a vector-valued sequence space, called the space of anisotropic $(s,q,r)$-summable sequences, that generalizes the classical space of $(s; q)$-mixed sequences (or mixed $(s; q)$-summable sequences). Furthermore, we define two classes of linear operators involving this new space and one of them generalizes the class of $(s; q) $-mixed linear operators due A. Pietsch. Some characterizations, inclusion results and a Pietsch domination-type theorem are presented for these classes. It is worth mentioning that some of these results are new even in the particular cases of mixed summable sequences and mixed summing operators.

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BibTeX RIS

Jamilson R. Campos, Renato Macedo, Joedson Santos. 2022-04-18. An anisotropic summability and mixed sequences. https://arxiv.org/abs/2204.08313

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