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#### Article: Linear maps relating different unitary similarity orbits or different generalized numerical ranges

Title Linear maps relating different unitary similarity orbits or different generalized numerical ranges Li, CKTsing, NK 1995 Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa Linear Algebra And Its Applications, 1995, v. 223-224 C, p. 463-481 How to Cite? Let M be the complex linear space Mn of n × n complex matrices or the real linear space Hn of n × n hermitian matrices. For C ∈ M, its unitary similarity orbit is the set. U(C) = {UCU*; U unitary. and its circular unitary similarity orbit is the set. V(C) = {μX : μ ∈ F, |μ| = 1, X ∈ U(C)}. where F is the scalar field C or R according as M = Mn or M = Hn. Related to U(C) and V(C) are the C-numerical range and the C-numerical radius of A ∈ M defined by. Wc(A) = {tr(AX) : X ∈U(C)}. and. rC(A)=max{|z|:z∈WC(A)},. respectively. Let C, D ∈ Hn, we study the linear operators T on M satisfying one of the following properties: (I) WD(T(A)) = WC(A) for all A ∈ M, (II) rD(T(A)) = rC(A) for all A ∈ M, (III) T(U(D)) = U(C), (IV) T(V(D)) = V(C). In particular, we determine the conditions on C and D for the existence of a linear operator T on M satisfying any one of the conditions (I)-(IV), and characterize such an operator if it exists. © 1995. http://hdl.handle.net/10722/156100 0024-37952015 Impact Factor: 0.9652015 SCImago Journal Rankings: 0.837

DC FieldValueLanguage
dc.contributor.authorLi, CKen_US
dc.contributor.authorTsing, NKen_US
dc.date.accessioned2012-08-08T08:40:24Z-
dc.date.available2012-08-08T08:40:24Z-
dc.date.issued1995en_US
dc.identifier.citationLinear Algebra And Its Applications, 1995, v. 223-224 C, p. 463-481en_US
dc.identifier.issn0024-3795en_US
dc.identifier.urihttp://hdl.handle.net/10722/156100-
dc.description.abstractLet M be the complex linear space Mn of n × n complex matrices or the real linear space Hn of n × n hermitian matrices. For C ∈ M, its unitary similarity orbit is the set. U(C) = {UCU*; U unitary. and its circular unitary similarity orbit is the set. V(C) = {μX : μ ∈ F, |μ| = 1, X ∈ U(C)}. where F is the scalar field C or R according as M = Mn or M = Hn. Related to U(C) and V(C) are the C-numerical range and the C-numerical radius of A ∈ M defined by. Wc(A) = {tr(AX) : X ∈U(C)}. and. rC(A)=max{|z|:z∈WC(A)},. respectively. Let C, D ∈ Hn, we study the linear operators T on M satisfying one of the following properties: (I) WD(T(A)) = WC(A) for all A ∈ M, (II) rD(T(A)) = rC(A) for all A ∈ M, (III) T(U(D)) = U(C), (IV) T(V(D)) = V(C). In particular, we determine the conditions on C and D for the existence of a linear operator T on M satisfying any one of the conditions (I)-(IV), and characterize such an operator if it exists. © 1995.en_US
dc.languageengen_US
dc.publisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laaen_US
dc.relation.ispartofLinear Algebra and Its Applicationsen_US
dc.titleLinear maps relating different unitary similarity orbits or different generalized numerical rangesen_US
dc.typeArticleen_US
dc.identifier.emailTsing, NK:nktsing@hku.hken_US
dc.identifier.authorityTsing, NK=rp00794en_US
dc.identifier.doi10.1016/0024-3795(95)00105-Z-
dc.identifier.scopuseid_2-s2.0-0039377776en_US
dc.identifier.hkuros20722-
dc.identifier.volume223-224en_US
dc.identifier.issueCen_US
dc.identifier.spage463en_US
dc.identifier.epage481en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridLi, CK=8048590800en_US
dc.identifier.scopusauthoridTsing, NK=6602663351en_US