A modern look at algebras of operators on Lp-spaces

The study of operator algebras on Hilbert spaces, and C∗-algebras in particular, is one of the most active areas within Functional Analysis. A natural generalization of these is to replace Hilbert spaces (which are L2-spaces) with Lp-spaces, for p∈[1,∞). The study of such algebras of operators is no...

Full description

Saved in:
Bibliographic Details
Published inExpositiones mathematicae Vol. 39; no. 3; pp. 420 - 453
Main Author Gardella, Eusebio
Format Journal Article
LanguageEnglish
Published Elsevier GmbH 01.09.2021
Subjects
[formula omitted]-Cuntz algebras
[formula omitted]-spaces
Banach algebras
Topological groups
secondary
Lp-spaces
Lp-Cuntz algebras
Banach algebras
primary
Topological groups
Online AccessGet full text

Cover

More Information
Summary:The study of operator algebras on Hilbert spaces, and C∗-algebras in particular, is one of the most active areas within Functional Analysis. A natural generalization of these is to replace Hilbert spaces (which are L2-spaces) with Lp-spaces, for p∈[1,∞). The study of such algebras of operators is notoriously more challenging, due to the very complicated geometry of Lp-spaces by comparison with Hilbert spaces. We give a modern overview of a research area whose beginnings can be traced back to the 50’s, and that has seen renewed attention in the last decade through the infusion of new techniques. The combination of these new ideas with old tools was the key to answer some long standing questions. Among others, we provide a description of all unital contractive homomorphisms between algebras of p-pseudofunctions of groups.
ISSN:0723-0869
1878-0792
DOI:10.1016/j.exmath.2020.10.003