Characterizations of derivations and Jordan derivations on Banach algebras

By Fangyan Lu. 2009

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Abstract Let A be an algebra and M be an A -bimodule. Let X be in A and δ : A → M be a linear map which satisfies δ ( AB ) = δ ( A ) B + A δ ( B ) for all A , B ∈ A with AB = X . It is shown that δ is a Jordan derivation if δ is continuous and X is left (or right) invertible. Also, it is shown that δ is a derivation if X is idempotent such that for M ∈ M the condition X A ( I - X ) M = 0 implies ( I - X ) M = 0 and the condition MX A ( I - X ) = 0 implies MX = 0 .

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/881d5f922f1f11fed5b23c46f6d52e7330ab0720