On subnormal operators whose spectrum are multiply connected domains
type: Item
instance of: scholarly article
title: On subnormal operators whose spectrum are multiply connected domains
zbMATH Open document ID: 1230.47041
author: Jianyong Qiao
author: Sumit K. Garg
published in: The New York Journal of Mathematics
publication date: 2011-08-02T00:00:00Z
full work available at URL: https://eudml.org/doc/229339
full work available at URL: 17a-11.html
review text: Let \(\Omega\subset \mathbb{C}\) be a connected bounded domain with finitely many holes and boundary which consists of disjoint simple closed rectifiable nontrivial Jordan curves. Let \(\mu\) be a finite Borel-measure on \(\partial \Omega\) and let \(H\) be an \(M_z\) invariant subspace of \(L^2(\mu, \ell^2)\). Set \(T=M_z|_H\). The main result of the paper says that the multiplicity function of a minimal normal extension of \(T\) equals \(-\operatorname{ind}(T-\lambda)~\mu\)-a.e.\ if \(T\) is a pure subnormal operator such that \(\sigma(T)=\overline{\Omega}\). Here, \(\lambda \in \Omega\) is fixed. Moreover, it is shown that there exist \(f_1, \dots, f_n \in H\) such that \(H\) is spanned by functions \(rf_j\), where \(r\) runs through the set of rational functions with poles outside \(\sigma(T)\) and \(j=1, \dots, n\).
reviewed by: Janko Bračič
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 46E40
zbMATH DE Number: 5935424
zbMATH Keywords: subnormal operators
zbMATH Keywords: index
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5935424