Generalized Jordan Semitriple Maps on Hilbert Space Effect Algebras

Generalized Jordan Semitriple Maps on Hilbert Space Effect Algebras

Let ℰ(H) be the Hilbert space effect algebra on a Hilbert space H with dim⁡H≥3, α,β two positive numbers with 2α+β≠1 and Φ:ℰ(H)→ℰ(H) a bijective map. We show that if Φ(AαBβAα)=Φ(A)αΦ(B)βΦ(A)α holds for all A,B∈ℰ(H), then there exists a unitary or an antiunitary operator U on H such that Φ(A)=UAU* fo...

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Main Authors: Qing Yuan, Kan He
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2014/216713
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spelling doaj-8979f1464de246f097176bc7f68eeb222021-07-02T02:29:24ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392014-01-01201410.1155/2014/216713216713Generalized Jordan Semitriple Maps on Hilbert Space Effect AlgebrasQing Yuan0Kan He1College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, ChinaCollege of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, ChinaLet ℰ(H) be the Hilbert space effect algebra on a Hilbert space H with dim⁡H≥3, α,β two positive numbers with 2α+β≠1 and Φ:ℰ(H)→ℰ(H) a bijective map. We show that if Φ(AαBβAα)=Φ(A)αΦ(B)βΦ(A)α holds for all A,B∈ℰ(H), then there exists a unitary or an antiunitary operator U on H such that Φ(A)=UAU* for every A∈ℰ(H).http://dx.doi.org/10.1155/2014/216713
collection DOAJ
language English
format Article
sources DOAJ
author Qing Yuan
Kan He
spellingShingle Qing Yuan
Kan He
Generalized Jordan Semitriple Maps on Hilbert Space Effect Algebras
Advances in Mathematical Physics
author_facet Qing Yuan
Kan He
author_sort Qing Yuan
title Generalized Jordan Semitriple Maps on Hilbert Space Effect Algebras
title_short Generalized Jordan Semitriple Maps on Hilbert Space Effect Algebras
title_full Generalized Jordan Semitriple Maps on Hilbert Space Effect Algebras
title_fullStr Generalized Jordan Semitriple Maps on Hilbert Space Effect Algebras
title_full_unstemmed Generalized Jordan Semitriple Maps on Hilbert Space Effect Algebras
title_sort generalized jordan semitriple maps on hilbert space effect algebras
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2014-01-01
description Let ℰ(H) be the Hilbert space effect algebra on a Hilbert space H with dim⁡H≥3, α,β two positive numbers with 2α+β≠1 and Φ:ℰ(H)→ℰ(H) a bijective map. We show that if Φ(AαBβAα)=Φ(A)αΦ(B)βΦ(A)α holds for all A,B∈ℰ(H), then there exists a unitary or an antiunitary operator U on H such that Φ(A)=UAU* for every A∈ℰ(H).
url http://dx.doi.org/10.1155/2014/216713
work_keys_str_mv AT qingyuan generalizedjordansemitriplemapsonhilbertspaceeffectalgebras
AT kanhe generalizedjordansemitriplemapsonhilbertspaceeffectalgebras
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