Maps Preserving Peripheral Spectrum of Generalized Jordan Products of Self-Adjoint Operators

Wen Zhang and Jinchuan Hou

Abstract and Applied Analysis, 2014, vol. 2014, 1-8

Abstract:

Let and be standard real Jordan algebras of self-adjoint operators on complex Hilbert spaces and , respectively. For , let be a fixed sequence with and assume that at least one of the terms in appears exactly once. Define the generalized Jordan product on elements in . Let be a map with the range containing all rank-one projections and trace zero-rank two self-adjoint operators. We show that satisfies that for all , where stands for the peripheral spectrum of , if and only if there exist a scalar and a unitary operator such that for all , or for all , where is the transpose of for an arbitrarily fixed orthonormal basis of . Moreover, whenever is odd.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:192040

DOI: 10.1155/2014/192040

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