Isometries of non-self-adjoint operator algebras
type: Item
instance of: scholarly article
title: Isometries of non-self-adjoint operator algebras
zbMATH Open document ID: 0713.46043
DOI: 10.1016/0022-1236(90)90085-Y
author: Jonathan Arazy
author: Baruch Solel
published in: Journal of Functional Analysis
publication date: 1990-01-01T00:00:00Z
review text: The paper is devoted to the study of isometries of certain non selfadjoint operator algebras by means of the structure of the complete holomorphic vector fields on their unit balls and the associated partial Jordan triple product. A family \({\mathfrak N}\) of projections in B(H) is called a nest if it is totally ordered and contains 0 and I. \({\mathfrak N}\) is said to be complete if it is closed in the strong operator topology. The nest algebra alg \({\mathfrak N}\) associated with \({\mathfrak N}\) is defined as \[ alg {\mathfrak N}=\{T\in B(H):\;(I-P)TP=0\text{ for all } P\in {\mathfrak N}\}. \] The main result of the paper says that if \({\mathfrak N}\) and \({\mathfrak M}\) are complete nests of projection in B(H) then any linear isometry between alg \({\mathfrak N}\) and alg \({\mathfrak M}\) is of the form \(T\mapsto UTW\) or \(T\mapsto UJT^*JW\), where U, V are suitable unitary operators and J a fixed involution of H.
Mathematics Subject Classification ID: 46L70
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 4173684
zbMATH Keywords: isometries of certain non selfadjoint operator algebras
zbMATH Keywords: structure of the complete holomorphic vector fields on their unit
zbMATH Keywords: partial Jordan triple product
zbMATH Keywords: nest algebra
zbMATH Keywords: complete nests
reviewed by: Sh. A. Ayupov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4173684