Maps Preserving Schatten p -Norms of Convex Combinations
Joint Authors
Tsai, Ming-Cheng
Zhang, Jun
Wong, Ngai-Ching
Kuo, Li-Wei
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-12-31
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
We study maps ϕ of positive operators of the Schatten p -classes ( 1 < p < + ∞ ), which preserve the p -norms of convex combinations, that is, ∥ t ρ + ( 1 - t ) σ ∥ p = ∥ t ϕ ( ρ ) + ( 1 - t ) ϕ ( σ ) ∥ p , ∀ ρ , σ ∈ ? p + ( H ) 1 , t ∈ [ 0,1 ] .
They are exactly those carrying the form ϕ ( ρ ) = U ρ U * 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.
American Psychological Association (APA)
Kuo, Li-Wei& Tsai, Ming-Cheng& Wong, Ngai-Ching& Zhang, Jun. 2013. Maps Preserving Schatten p -Norms of Convex Combinations. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-5.
https://search.emarefa.net/detail/BIM-1033821
Modern Language Association (MLA)
Kuo, Li-Wei…[et al.]. Maps Preserving Schatten p -Norms of Convex Combinations. Abstract and Applied Analysis No. 2014 (2014), pp.1-5.
https://search.emarefa.net/detail/BIM-1033821
American Medical Association (AMA)
Kuo, Li-Wei& Tsai, Ming-Cheng& Wong, Ngai-Ching& Zhang, Jun. Maps Preserving Schatten p -Norms of Convex Combinations. Abstract and Applied Analysis. 2013. Vol. 2014, no. 2014, pp.1-5.
https://search.emarefa.net/detail/BIM-1033821
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033821