Geodesic
Characterizations of Jordan derivations on triangular rings: additive maps Jordan derivable at idempotents
The electronic journal of linear algebra, Tome 21 (2010), pp. 28-42.

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

Summary: Let T be a triangular ring. An additive map $\delta $from T into itself is said to be Jordan derivable at an element Z $\in T$ if $\delta (A)$B + A$\delta (B) + \delta (B)$A + B$\delta (A) = \delta $(AB + BA) for any A, B $\in T$ with AB + BA = Z. An element Z $\in T$ is called a Jordan all-derivable point of T if every additive map Jordan derivable at Z is a Jordan derivation. In this paper, we show that some idempotents in T are Jordan all-derivable points. As its application, we get the result that for any nest N in a factor von Neumann algebra R, every nonzero idempotent element Q satisfying P Q = Q, QP = P for some projection P $\in N$ is a Jordan all-derivable point of the nest subalgebra AlgN of R.
Classification : 16W25, 47B49
Keywords: Jordan derivations, triangular rings, nest algebras 
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     author = {An, Runling and Hou, Jinchuan},
     title = {Characterizations of {Jordan} derivations on triangular rings: additive maps {Jordan} derivable at idempotents},
     journal = {The electronic journal of linear algebra},
     pages = {28--42},
     publisher = {mathdoc},
     volume = {21},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2010__21__a9/}
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An, Runling; Hou, Jinchuan. Characterizations of Jordan derivations on triangular rings: additive maps Jordan derivable at idempotents. The electronic journal of linear algebra, Tome 21 (2010), pp. 28-42. http://geodesic.mathdoc.fr/item/ELA_2010__21__a9/