Title : ( Maps preserving quadratic product between positive cones of JBW-algebras )
Authors: MOZHDEH SAFARIZADEH ,
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Abstract
LetAbe a JBW-algebra. For a ∈ A, let U_a denote the quadratic operator defined by U_a(b) = 2a ◦ (a ◦ b) − a^2 ◦ b (b ∈ A). We show that if A has no abelian direct summand, then every bijection φ from the positive cone of A onto the positive cone of a JBW-algebra B satisfying φ(U_ab) = U_φ(a)(φ(b)) for all positive elements a, b ∈ A extends to a Jordan isomorphism from A onto B.
Keywords
, JBW, algebra; quadratic operator; quadratic product; preserver mapping
@article{paperid:1074466,
author = {SAFARIZADEH, MOZHDEH},
title = {Maps preserving quadratic product between positive cones of JBW-algebras},
journal = {Linear and Multilinear Algebra},
year = {2019},
volume = {69},
number = {3},
month = {April},
issn = {0308-1087},
pages = {471--488},
numpages = {17},
keywords = {JBW-algebra; quadratic operator; quadratic product; preserver mapping},
}
%0 Journal Article
%T Maps preserving quadratic product between positive cones of JBW-algebras
%A SAFARIZADEH, MOZHDEH
%J Linear and Multilinear Algebra
%@ 0308-1087
%D 2019
