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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 |
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Authors | |
Issue Date | 1995 |
Publisher | Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa |
Citation | Linear Algebra And Its Applications, 1995, v. 223-224 C, p. 463-481 How to Cite? |
Abstract | 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. |
Persistent Identifier | http://hdl.handle.net/10722/156100 |
ISSN | 2023 Impact Factor: 1.0 2023 SCImago Journal Rankings: 0.837 |
DC Field | Value | Language |
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dc.contributor.author | Li, CK | en_US |
dc.contributor.author | Tsing, NK | en_US |
dc.date.accessioned | 2012-08-08T08:40:24Z | - |
dc.date.available | 2012-08-08T08:40:24Z | - |
dc.date.issued | 1995 | en_US |
dc.identifier.citation | Linear Algebra And Its Applications, 1995, v. 223-224 C, p. 463-481 | en_US |
dc.identifier.issn | 0024-3795 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156100 | - |
dc.description.abstract | 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. | en_US |
dc.language | eng | en_US |
dc.publisher | Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa | en_US |
dc.relation.ispartof | Linear Algebra and Its Applications | en_US |
dc.title | Linear maps relating different unitary similarity orbits or different generalized numerical ranges | en_US |
dc.type | Article | en_US |
dc.identifier.email | Tsing, NK:nktsing@hku.hk | en_US |
dc.identifier.authority | Tsing, NK=rp00794 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1016/0024-3795(95)00105-Z | - |
dc.identifier.scopus | eid_2-s2.0-0039377776 | en_US |
dc.identifier.hkuros | 20722 | - |
dc.identifier.volume | 223-224 | en_US |
dc.identifier.issue | C | en_US |
dc.identifier.spage | 463 | en_US |
dc.identifier.epage | 481 | en_US |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Li, CK=8048590800 | en_US |
dc.identifier.scopusauthorid | Tsing, NK=6602663351 | en_US |
dc.identifier.issnl | 0024-3795 | - |