On the joint spectrum for n-tuples of hyponormal operators
type: Item
instance of: scholarly article
title: On the joint spectrum for n-tuples of hyponormal operators
zbMATH Open document ID: 0602.47017
author: Dianzhou Zhang
author: Danrun Huang
published in: Chinese Annals of Mathematics. Series B
publication date: 1986-01-01T00:00:00Z
review text: Let \(A=(A_ 1,...,A_ n)\) be an n-tuple of doubly commuting hyponormal operators. It is proved that: 1. The joint spectrum of A has a Cartesian decomposition: \(Re[Sp(A)]=S_ p(Re A)\), \(Im[Sp(A)]=Sp(Im A);\) 2. The joint resolvent of A satisfies the growth condition: \(\| (A- s)^{\wedge}\| =1/dist(z,Sp(A));\) 3. If \(0\not\in \sigma (A_ i)\), \(i=1,2,...,n\), then \(\| A\| =r_{sp}(A)\).
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 3971557
zbMATH Keywords: doubly commuting hyponormal operators
zbMATH Keywords: Cartesian decomposition
zbMATH Keywords: joint resolvent
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3971557