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July 2016 Characterizations of Jordan left derivations on some algebras
Guangyu An, Yana Ding, Jiankui Li
Banach J. Math. Anal. 10(3): 466-481 (July 2016). DOI: 10.1215/17358787-3599675


A linear mapping δ from an algebra A into a left A-module M is called a Jordan left derivation if δ(A2)=2Aδ(A) for every AA. We prove that if an algebra A and a left A-module M satisfy one of the following conditions—(1) A is a C-algebra and M is a Banach left A-module; (2) A=AlgL with {L:LJL}=(0) and M=B(X); and (3) A is a commutative subspace lattice algebra of a von Neumann algebra B and M=B(H)—then every Jordan left derivation from A into M is zero. δ is called left derivable at GA if δ(AB)=Aδ(B)+Bδ(A) for each A,BA with AB=G. We show that if A is a factor von Neumann algebra, G is a left separating point of A or a nonzero self-adjoint element in A, and δ is left derivable at G, then δ0.


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Guangyu An. Yana Ding. Jiankui Li. "Characterizations of Jordan left derivations on some algebras." Banach J. Math. Anal. 10 (3) 466 - 481, July 2016.


Received: 1 April 2015; Accepted: 18 August 2015; Published: July 2016
First available in Project Euclid: 13 May 2016

zbMATH: 1351.47027
MathSciNet: MR3504180
Digital Object Identifier: 10.1215/17358787-3599675

Primary: 47B47
Secondary: 47C15 , 47L35

Keywords: $C^{*}$-algebra , Jordan left derivation , left derivable point , left separating point

Rights: Copyright © 2016 Tusi Mathematical Research Group


Vol.10 • No. 3 • July 2016
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