Spectrum of Weighted Composition Operators. Part II. Weighted composition operators on subspaces of Banach lattices

TL;DR

This paper characterizes the spectrum of weighted composition operators on certain subspaces of Banach lattices, including applications to Hardy spaces, revealing how these operators preserve the order structure.

Contribution

It provides a detailed spectral analysis of weighted d-isomorphisms on Banach lattice subspaces that retain key order properties, extending previous results to new contexts.

Findings

Spectrum characterized for weighted d-isomorphisms on Banach lattice subspaces

Includes examples like weighted isometries of Hardy spaces

Demonstrates preservation of order structure in spectral properties

Abstract

We describe the spectrum of weighted $d$-isomorphisms of Banach lattices restricted on closed subspaces that are "rich" enough to preserve some "memory" of the order structure of the original lattice. The examples include (but are not limited to) weighted isometries of Hardy spaces on the polydisk and unit ball in $\mathds{C}^n$.