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

TL;DR

This paper offers a unified framework for analyzing Banach ideals of linear and multilinear operators based on their effects on vector-valued sequences, exploring stability properties of these classes.

Contribution

It introduces a comprehensive approach to study Banach ideals via sequence transformations, extending the understanding of linear and multilinear operator stability.

Findings

Unified approach to Banach ideals of operators

Characterization of operator classes through sequence transformations

Analysis of stability properties of vector-valued sequence classes

Abstract

In this paper we provide a unifying approach to the study of Banach ideals of linear and multilinear operators defined, or characterized, by the transformation of vector-valued sequences. We investigate and apply the linear and multilinear stabilities of some frequently used classes of vector-valued sequences.