Hardy algebras associated with W^*-correspondences (point evaluation and Schur class functions)

2004/04/18 by Paul S. Muhly, Muhly, Paul S., Baruch Solel +1
Mathematics · #46L08 #46L53 #47A48 #47A57 #47L55 #47L65 #47L75 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA #msc:46L08 #msc:46L53 #msc:47A48 #msc:47A57 #msc:47L55 #msc:47L65 #msc:47L75

paper · pdf · doi:10.48550/arxiv.math/0404317

Expository, 28 pages

arxiv created 2004/04/18 · openalex publication_date 2004/04/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is primarily an exposition of our work on Hardy algebras associated with W^*-correspondences with an emphasis on interpolation results (a generalized Nevanlinna-Pick theorem) and the concepts of Schur class operator functions (and realizations). We describe in detail the construction of the Hardy algebras, its representations and the important concepts of duality and point evaluation. Many examples are provided.

Related

• Duality of W^*-correspondences and applications
• Schur Class Operator Functions and Automorphisms of Hardy Algebras
• Hardy Algebras, W*-Correspondences and Interpolation Theory
• Multivariable operator-valued Nevanlinna-Pick interpolation: a survey
• Canonical Models for Representations of Hardy Algebras