Bounded point evaluation for a finitely multicyclic commuting tuple of operators
type: Item
instance of: scholarly article
title: Bounded point evaluation for a finitely multicyclic commuting tuple of operators
zbMATH Open document ID: 1461.47001
author: Shailesh Trivedi
published in: Bulletin des Sciences Mathématiques
publication date: 2020-08-06T00:00:00Z
review text: The author introduces and establishes the basic properties of bounded point evaluations for a finitely multicyclic commuting \(d\)-tuple \(T=(T_1,\dots, T_d)\) of bounded linear operators on a complex separable Hilbert space \(H\). He shows that the set \(bpe(T)\) of all bounded point evaluations for \(T\) is a unitary invariant and characterizes it in terms of the dimension of the joint cokernel of \(T\). Furthermore, he characterizes the set of all analytic bounded point evaluations for \(T\), which is the largest open subset of \(bpe(T)\) on which all the elements of \(H\) are analytic. As an application, he describes the set of all analytic bounded point evaluations for toral and spherical isometries, and also derives an analytic model of a commuting \(d\)-tuple of composition operators.
reviewed by: Abdellatif Bourhim
Mathematics Subject Classification ID: 47A13
Mathematics Subject Classification ID: 46E22
Mathematics Subject Classification ID: 46E40
zbMATH DE Number: 7229228
zbMATH Keywords: bounded point evaluation
zbMATH Keywords: operator-valued reproducing kernel
zbMATH Keywords: finitely multicyclic
MaRDI profile type: Publication
full work available at URL: j.bulsci.2020.102875
OpenAlex ID: W3026427872
cites work: Q3154380
cites work: Q4422005
cites work: Analytic models for commuting operator tuples on bounded symmetric domains
cites work: Subnormality of unbounded composition operators over one-circuit directed graphs: exotic examples
cites work: An operator-valued kernel associated with a commuting tuple of Hilbert space operators
cites work: Multishifts on directed Cartesian products of rooted directed trees
cites work: Q4000087
cites work: Multivariable Bergman shifts and Wold decompositions
cites work: Q4679512
cites work: Unitary equivalence of operator-valued multishifts
cites work: Q3868344
cites work: Q4951127
cites work: The interior of bounded point evaluations for rationally cyclic operators
cites work: Analytic bounded point evaluations for rationally cyclic operators on Banach spaces
cites work: Spectral radius formula for commuting Hilbert space operators
cites work: An introduction to the theory of reproducing kernel Hilbert spaces
cites work: Q4059478
cites work: Wold-type decompositions and wandering subspaces for operators close to isometries
cites work: Reproducing kernels and operators with a cyclic vector. I
cites work: Approximation in the mean by polynomials
cites work: \(H^2(\mu)\) spaces and bounded point evaluations
cites work: Q3213702
cites work: Q4285693
DOI: 10.1016/J.BULSCI.2020.102875
description: scientific article; zbMATH DE number 7229228