Disjointly homogeneous Banach lattices and applications

TL;DR

This survey explores disjointly homogeneous Banach lattices, analyzing their structural properties and demonstrating their usefulness in studying operator compactness, providing a unified approach to existing results.

Contribution

It offers a comprehensive analysis of disjointly homogeneous Banach lattices and introduces their application in understanding operator compactness.

Findings

Structural properties of disjointly homogeneous Banach lattices are characterized.

These spaces facilitate a unified framework for studying operator compactness.

The survey connects lattice properties with operator theory results.

Abstract

This is a survey on disjointly homogeneous Banach lattices and their applicactions. Several structural properties of this class are analyzed. In addition we show how these spaces provide a natural framework for studying the compactness of powers of operators allowing for a unified treatment of well-known results.