On Hermitian operator in tensor product space
type: Item
instance of: scholarly article
title: On Hermitian operator in tensor product space
zbMATH Open document ID: 0638.47017
published in: Chinese Annals of Mathematics. Series B
publication date: 1987-01-01T00:00:00Z
review text: Let V be an n-dimensional Hilbert space, \(A_ i\) \((i=1,...,n)\) linear operators on V and \(L=A_ 1\otimes...\otimes A_ n\) their tensor product acting in the \(n^{th}\) tensor power of V. The numerical range of L is defined as the set of (Lx,x), where \(x=x_ 1\otimes...\otimes x_ n\) and \((x_ 1,...,x_ n)\) spans the orthonormal bases of V. It is proved that, for \(n\geq 3\), the numerical range of L is real if and only if L is hermitian.
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 47A12
zbMATH DE Number: 4040620
zbMATH Keywords: tensor product
zbMATH Keywords: numerical range
zbMATH Keywords: orthonormal bases
author: Shu-An Hu
reviewed by: Nicolae Angelescu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4040620