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CHARACTERIZATIONS OF JORDAN DERIVATIONS ON STRONGLY DOUBLE TRIANGLE SUBSPACE LATTICE ALGEBRAS

Part of: Special classes of linear operators

Published online by Cambridge University Press:  21 July 2011

YUN-HE CHEN  and
JIAN-KUI LI
YUN-HE CHEN
Affiliation:
Department of Mathematics, East China University of Science and Technology, Shanghai 200237, PR China (email: [email protected])
JIAN-KUI LI*
Affiliation:
Department of Mathematics, East China University of Science and Technology, Shanghai 200237, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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Let 𝒟 be a strongly double triangle subspace lattice on a nonzero complex reflexive Banach space X and let δ:Alg 𝒟→Alg 𝒟 be a linear mapping. We show that δ is Jordan derivable at zero, that is, δ(AB+BA)=δ(A)B+Aδ(B)+δ(B)A+Bδ(A) whenever AB+BA=0 if and only if δ has the form δ(A)=τ(A)+λA for some derivation τ and some scalar λ. We also show that if the dimension of X is greater than 2, then δ satisfies δ(AB+BA)=δ(A)B+Aδ(B)+δ(B)A+Bδ(A) whenever AB=0 if and only if δ is a derivation.

Keywords

derivationJordan derivationsubspace lattice

MSC classification

Secondary: 47B47: Commutators, derivations, elementary operators, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 2 , October 2011 , pp. 300 - 309
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

This work is supported by NSF of China.

References

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