Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 10, Number 3 (2016), 466-481.
Characterizations of Jordan left derivations on some algebras
A linear mapping from an algebra into a left -module is called a Jordan left derivation if for every . We prove that if an algebra and a left -module satisfy one of the following conditions—(1) is a -algebra and is a Banach left -module; (2) with and ; and (3) is a commutative subspace lattice algebra of a von Neumann algebra and —then every Jordan left derivation from into is zero. is called left derivable at if for each with . We show that if is a factor von Neumann algebra, is a left separating point of or a nonzero self-adjoint element in , and is left derivable at , then .
Banach J. Math. Anal., Volume 10, Number 3 (2016), 466-481.
Received: 1 April 2015
Accepted: 18 August 2015
First available in Project Euclid: 13 May 2016
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An, Guangyu; Ding, Yana; Li, Jiankui. Characterizations of Jordan left derivations on some algebras. Banach J. Math. Anal. 10 (2016), no. 3, 466--481. doi:10.1215/17358787-3599675. https://projecteuclid.org/euclid.bjma/1463153911