$(p,q)$-regular operators between Banach lattices

TL;DR

This paper investigates $(p,q)$-regular operators between quasi-Banach lattices, providing a dual tensor norm representation, factorization results, and an extension theorem, advancing the understanding of operator theory in Banach lattices.

Contribution

It introduces a dual tensor norm representation for $(p,q)$-regular operators and establishes new factorization and extension results in Banach lattice theory.

Findings

Representation of $(p,q)$-regular operators as dual of a tensor norm

New Marcinkiewicz-Zygmund type inequalities for Banach function spaces

Extension theorem for $(q, abla)$-regular operators on subspaces of $L_q$

Abstract

We study the class of $(p,q)$-regular operators between quasi-Banach lattices. In particular, a representation of this class as the dual of a certain tensor norm for Banach lattices is given. We also provide some factorization results for $(p,q)$-regular operators yielding new Marcinkiewicz-Zygmund type inequalities for Banach function spaces. An extension theorem for $(q, \infty)$-regular operators defined on a subspace of $L_q$ is also given.