Ideals of mid p-summing operators: a tensor product approach

TL;DR

This paper investigates mid p-summing operator ideals using tensor product techniques, providing new representations and characterizations of these operators and their adjoints in the context of tensor norms and sequence spaces.

Contribution

It introduces a tensor product approach to represent mid p-summing operator ideals and characterizes their adjoints via dual space transformations.

Findings

Representation of mid p-summing ideals by tensor norms

Characterization of adjoints of weakly and absolutely mid p-summing operators

Use of duals of mid p-summable sequences in tensor norm definitions

Abstract

In this article, we study the ideals of mid $p$-summing operators. We obtain representation of these operator ideals by tensor norms. These tensor norms are defined by using a particular kind of sequential dual of the class of mid $p$-summable sequences. As a consequence, we prove a characterization of the adjoints of weakly and absolutely mid $p$-summing operators in terms of the operators that are defined by the transformation of dual spaces of certain vector-valued sequence spaces.