Journal of the Korean Mathematical Society, ( ISI ), Volume (2), No (54), Year (2016-12) , Pages (1-10)

Title : ( Maps preserving some multiplicative structure on standard Jordan operator algebras )

Authors: somaye ghorbani poor , Shirin Hejazian ,

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Let A be a unital real standard Jordan operator algebra acting on a Hilbert space H of dimension at least 2. We show that every bijection \phi on A satisfying phi(a^2 o b) = \phi(a)^2 o \phi(b) is of the form \phi = e \psi where psi is an automorphism on A and e=1 or -1. As a consequence if A is the real algebra of all self-adjoint operators on a Hilbert space H, then there exists a unitary or conjugate unitary operator u on H such that ph(a) = euau* for all a in A.

Keywords

, standard Jordan operator algebra, preserver map, Jordan
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@article{paperid:1060608,
author = {Ghorbani Poor, Somaye and Hejazian, Shirin},
title = {Maps preserving some multiplicative structure on standard Jordan operator algebras},
journal = {Journal of the Korean Mathematical Society},
year = {2016},
volume = {2},
number = {54},
month = {December},
issn = {0304-9914},
pages = {1--10},
numpages = {9},
keywords = {standard Jordan operator algebra; preserver map; Jordan product},
}

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%0 Journal Article
%T Maps preserving some multiplicative structure on standard Jordan operator algebras
%A Ghorbani Poor, Somaye
%A Hejazian, Shirin
%J Journal of the Korean Mathematical Society
%@ 0304-9914
%D 2016

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