Abstract and Applied Analysis

Maps Preserving Schatten p -Norms of Convex Combinations

David Li-Wei Kuo, Ming-Cheng Tsai, Ngai-Ching Wong, and Jun Zhang

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Abstract

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 𝒮 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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 520795, 5 pages.

Dates
First available in Project Euclid: 26 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1395857998

Digital Object Identifier
doi:10.1155/2014/520795

Mathematical Reviews number (MathSciNet)
MR3166627

Zentralblatt MATH identifier
07022546

Citation

Kuo, David Li-Wei; Tsai, Ming-Cheng; Wong, Ngai-Ching; Zhang, Jun. Maps Preserving Schatten $p$ -Norms of Convex Combinations. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 520795, 5 pages. doi:10.1155/2014/520795. https://projecteuclid.org/euclid.aaa/1395857998


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