Linear operators preserving the (p,q)-numerical range
type: Item
instance of: scholarly article
title: Linear operators preserving the (p,q)-numerical range
zbMATH Open document ID: 0655.15025
DOI: 10.1016/0024-3795(83)90133-7
author: Chi-Kwong Li
author: Bit-Shun Tam
author: Nam-Kiu Tsing
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: Let \(C_{m\times n},H_ n\) and \(U_ n\) denote respectively the space of complex \(m\times n\) matrices, the space of Hermitian \(n\times n\) matrices, and the group of unitary matrices in \(C_{n\times n}\). Let p,q,n be integers such that \(1\leq p\leq q\leq n\). For \(A\in C_{n\times n}\) the (p,q)-numerical range of A is defined to be the set \(W_{p,q}(A)=\{trC_ p(J_ qUAU^*):\) \(U\in U_ n\}\), where \(C_ p(A)\) denote the p-th compound matrix of A and \(J_ q=I_ q\oplus O_{n-q}\). The authors consider the problem of determining all linear operators \(T: C_{n\times n}\to C_{n\times n}\) (or \(H_ n\to H_ n)\) such that \(W_{p,q}(T(A))=W_{p,q}(A).\)
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A04
zbMATH DE Number: 4069099
zbMATH Keywords: (p,q)-numerical range
reviewed by: Shaokuan Li
MaRDI profile type: Publication
full work available at URL: 0024-3795(83)90133-7
OpenAlex ID: W2003530947
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description: scientific article; zbMATH DE number 4069099