Characterizations of Lie Higher Derivations on J-Subspace Lattice Algebras

2016/10/07 by Dong Han, Feng Wei, Han, Dong +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.1610.02188

Abstract

Let L be a J-subspace lattice on a Banach space X over the real or complex field \mathbbF and AlgL be the associated J-subspace lattice algebras. In this paper, we characterize the structure of a family \L_n\_n=0^∞: AlgL→ AlgL of linear mappings satisfying the condition L_n([A, B])=∑_i+j=n[L_i(A), L_j(B)] for any A, B\inAlgL with AB = 0. Moreover, the family \L_n\_n=0^∞: AlgL→ AlgL of linear mappings satisfying L_n([A, B]_ξ)=∑_i+j=n[L_i(A), L_j(B)]_ξ for any A, B\inAlgL with AB = 0 and 1≠ ξ∈ \mathbbF is also considered in the current work.

Citations

• Characterizations of Lie derivations of B ( X )
• Characterizations of Lie derivations of triangular algebras

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