Maps Preserving Schatten p-Norms of Convex Combinations
We study maps ϕ of positive operators of the Schatten p-classes (1<p<+∞), which preserve the p-norms of convex combinations, that is, ∥tρ+(1-t)σ∥p=∥tϕ(ρ)+(1-t)ϕ(σ)∥p, ∀ρ,σ∈𝒮p+(H)1, t∈[0,1]. They are exactly those carrying the form ϕ(ρ)=UρU* for a unitary or antiunitary U. In the case p=...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/520795 |
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| author | David Li-Wei Kuo Ming-Cheng Tsai Ngai-Ching Wong Jun Zhang |
| author_facet | David Li-Wei Kuo Ming-Cheng Tsai Ngai-Ching Wong Jun Zhang |
| author_sort | David Li-Wei Kuo |
| collection | DOAJ |
| description | We study maps ϕ of positive operators of the
Schatten p-classes (1<p<+∞), which preserve the p-norms of convex
combinations, that is, ∥tρ+(1-t)σ∥p=∥tϕ(ρ)+(1-t)ϕ(σ)∥p, ∀ρ,σ∈𝒮p+(H)1, t∈[0,1]. They are exactly those carrying the form ϕ(ρ)=UρU* for a unitary or antiunitary U. In the case p=2, we have the same conclusion whenever it just holds ∥ρ+σ∥2=∥ϕ(ρ)+ϕ(σ)∥2 for all the positive Hilbert-Schmidt class operators ρ,σ of norm 1. Some examples are demonstrated. |
| format | Article |
| id | doaj-art-b292eb66fe4f46ce887713bfdd879660 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b292eb66fe4f46ce887713bfdd8796602025-08-20T03:39:21ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/520795520795Maps Preserving Schatten p-Norms of Convex CombinationsDavid Li-Wei Kuo0Ming-Cheng Tsai1Ngai-Ching Wong2Jun Zhang3Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 80424, TaiwanDepartment of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 80424, TaiwanDepartment of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 80424, TaiwanSchool of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, ChinaWe study maps ϕ of positive operators of the Schatten p-classes (1<p<+∞), which preserve the p-norms of convex combinations, that is, ∥tρ+(1-t)σ∥p=∥tϕ(ρ)+(1-t)ϕ(σ)∥p, ∀ρ,σ∈𝒮p+(H)1, t∈[0,1]. They are exactly those carrying the form ϕ(ρ)=UρU* for a unitary or antiunitary U. In the case p=2, we have the same conclusion whenever it just holds ∥ρ+σ∥2=∥ϕ(ρ)+ϕ(σ)∥2 for all the positive Hilbert-Schmidt class operators ρ,σ of norm 1. Some examples are demonstrated.http://dx.doi.org/10.1155/2014/520795 |
| spellingShingle | David Li-Wei Kuo Ming-Cheng Tsai Ngai-Ching Wong Jun Zhang Maps Preserving Schatten p-Norms of Convex Combinations Abstract and Applied Analysis |
| title | Maps Preserving Schatten p-Norms of Convex Combinations |
| title_full | Maps Preserving Schatten p-Norms of Convex Combinations |
| title_fullStr | Maps Preserving Schatten p-Norms of Convex Combinations |
| title_full_unstemmed | Maps Preserving Schatten p-Norms of Convex Combinations |
| title_short | Maps Preserving Schatten p-Norms of Convex Combinations |
| title_sort | maps preserving schatten p norms of convex combinations |
| url | http://dx.doi.org/10.1155/2014/520795 |
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