J -子空间格代数上中心化子和广义导子的刻画

Abstract

Abstract:

Let L be a J-subspace lattice on a Banach space X and AlgL the associated J-subspace lattice algebra. Assume that Φ: AlgL→AlgL is an additive map and dimK≥2 for every K∈J(L). It is shown that the following statements are equivalent: (1) Φ is a centralizer; (2) Φ sataisies Φ(A)B=AΦ(B)=0 whenever A, B∈AlgL with AB=0; (3) Φ satisfies Φ(A)B+Φ(B)A=AΦ(B)+B\Φ(A)=0 whenever A, B∈AlgL with AB+BA=0; (4) Φ satisfies Φ(A)BC+Φ(C)BA=ABΦ(C)+CBΦ(A)=0 whenever A, B∈AlgL with ABC+CBA=0. As an application, additive maps generalized derivable at zero on AlgL are characterized.

Key words: J-subspace lattice algebras, Centralizers, Generalized derivations

CLC Number:

47L35

QI Xiao-Fei. Characterization of Centralizers and Generalized Derivations on J-Subspace Lattice Algebras[J].Acta mathematica scientia,Series A, 2014, 34(2): 463-472.

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Characterization of Centralizers and Generalized Derivations on J-Subspace Lattice Algebras

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