Maps Preserving Peripheral Spectrum of Generalized Jordan Products of Self-Adjoint Operators
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-10-19
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
Let A1 and A2 be standard real Jordan algebras of self-adjoint operators on complex Hilbert spaces H1 and H2, respectively.
For k≥2, let (i1,…,im) be a fixed sequence with i1,…,im∈{1,…,k} and assume that at least one of the terms in (i1,…,im) appears exactly once.
Define the generalized Jordan product T1∘T2∘⋯∘Tk=Ti1Ti2⋯Tim+Tim⋯Ti2Ti1 on elements in Ai.
Let Φ:A1→A2 be a map with the range containing all rank-one projections and trace zero-rank two self-adjoint operators.
We show that Φ satisfies that σπ(Φ(A1)∘⋯∘Φ(Ak))=σπ(A1∘⋯∘Ak) for all A1,…,Ak, where σπ(A) stands for the peripheral spectrum of A, if and only if there exist a scalar c∈{-1,1} and a unitary operator U:H1→H2 such that Φ(A)=cUAU* for all A∈A1, or Φ(A)=cUAtU* for all A∈A1, where At is the transpose of A for an arbitrarily fixed orthonormal basis of H1.
Moreover, c=1 whenever m is odd.
American Psychological Association (APA)
Zhang, Wen& Hou, Jinchuan. 2014. Maps Preserving Peripheral Spectrum of Generalized Jordan Products of Self-Adjoint Operators. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1013454
Modern Language Association (MLA)
Zhang, Wen& Hou, Jinchuan. Maps Preserving Peripheral Spectrum of Generalized Jordan Products of Self-Adjoint Operators. Abstract and Applied Analysis No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-1013454
American Medical Association (AMA)
Zhang, Wen& Hou, Jinchuan. Maps Preserving Peripheral Spectrum of Generalized Jordan Products of Self-Adjoint Operators. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1013454
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013454