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Maps Preserving Schatten -Norms of Convex Combinations

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

Abstract

We study maps of positive operators of the Schatten -classes ( ), which preserve the -norms of convex combinations, that is, . They are exactly those carrying the form for a unitary or antiunitary . In the case , we have the same conclusion whenever it just holds for all the positive Hilbert-Schmidt class operators of norm . Some examples are demonstrated.

Suggested Citation

  • David Li-Wei Kuo & Ming-Cheng Tsai & Ngai-Ching Wong & Jun Zhang, 2014. "Maps Preserving Schatten -Norms of Convex Combinations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, January.
    • Handle: RePEc:hin:jnlaaa:520795
    DOI: 10.1155/2014/520795
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