Homogeneous tuples of multiplication operators on twisted Bergman spaces
type: Item
instance of: scholarly article
title: Homogeneous tuples of multiplication operators on twisted Bergman spaces
zbMATH Open document ID: 0867.47022
author: Bhaskar Bagchi
author: Gadadhar Misra
published in: Journal of Functional Analysis
publication date: 1997-08-04T00:00:00Z
review text: Let \(\Omega_{n,m}\) be the domain of all \(n\times m\) contractive complex matrices \((m\geq n\geq 1)\), and let \(B\) be the Bergman kernel on this domain. Let also \({\mathcal W}\) be the set of those \(\lambda\geq 0\) for which \(B^{\lambda/(m+n)}\) is the reproducing kernel of a functional space \({\mathcal H}^{(\lambda)}\) (which is called a twisted Bergman space). In this paper the authors study the \(mn\)-tuple \(M^{(\lambda)}\) of operators on \({\mathcal H}^{(\lambda)}\) whose components are the multiplications by the \(mn\)-coordinate functions. They are concerned with the problem of determining the set of those \(\lambda\in{\mathcal W}\) for which \(M^{(\lambda)}\) is bounded, and moreover, subnormal. Other problems, as for instance when the Taylor spectrum of \(M^{(\lambda)}\) is a \(k\)-spectral set, are also examined. Let us mention that most of the techniques developed in this paper apply to the larger class of bounded Cartan domains.
reviewed by: Florian-Horia Vasilescu
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47A13
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 871742
zbMATH Keywords: contractive complex matrices
zbMATH Keywords: Bergman kernel
zbMATH Keywords: Taylor spectrum
zbMATH Keywords: \(k\)-spectral set
zbMATH Keywords: Cartan domains
MaRDI profile type: Publication
OpenAlex ID: W1989757084
DOI: 10.1006/JFAN.1996.0026
description: scientific article; zbMATH DE number 871742