Geodesic
Linear maps preserving the idempotency of Jordan products of operators
The electronic journal of linear algebra, Tome 22 (2011), pp. 767-779.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $B(X )$ be the algebra of all bounded linear operators on a complex Banach space X and let I * (X ) be the set of non-zero idempotent operators in $B(X )$. A surjective map $\varphi : B(X ) \rightarrow B(X )$ preserves nonzero idempotency of the Jordan products of two operators if for every pair A, B $\in B(X )$, the relation AB + BA $\in I$ * (X ) implies $\varphi (A)\varphi (B) + \varphi (B)\varphi (A) \in I$ * (X ). In this paper, the structures of linear surjective maps on $B(X )$ preserving the nonzero idempotency of Jordan products of two operators are given.
Classification : 47B49
Keywords: Banach space, preserver, idempotent, Jordan product 
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     author = {Fang, Li},
     title = {Linear maps preserving the idempotency of {Jordan} products of operators},
     journal = {The electronic journal of linear algebra},
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     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/ELA_2011__22__a26/}
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Fang, Li. Linear maps preserving the idempotency of Jordan products of operators. The electronic journal of linear algebra, Tome 22 (2011), pp. 767-779. http://geodesic.mathdoc.fr/item/ELA_2011__22__a26/