An anisotropic summability and mixed sequences

TL;DR

This paper introduces a new vector-valued sequence space called anisotropic (s,q,r)-summable sequences, generalizing classical mixed sequence spaces, and studies associated linear operators with new characterization and domination results.

Contribution

It defines the anisotropic (s,q,r)-summable sequence space and extends the class of mixed linear operators, providing new characterizations and domination theorems.

Findings

Introduces anisotropic (s,q,r)-summable sequence space.

Provides new characterizations and inclusion results.

Establishes a Pietsch domination-type theorem for the new operators.

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.