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Journal of Function Spaces and Applications
Volume 2013, Article ID 407427, 11 pages
http://dx.doi.org/10.1155/2013/407427
Research Article

Characterizing Derivations on Von Neumann Algebras by Local Actions

Department of Mathematics, Shanxi University, Taiyuan 030006, China

Received 25 August 2013; Accepted 25 November 2013

Academic Editor: P. Veeramani

Copyright © 2013 Xiaofei Qi and Jia Ji. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be any von Neumann algebra without central summands of type and a core-free projection with the central carrier . For any scalar , it is shown that every additive map on satisfies whenever if and only if (1) , , where is an additive derivation and is a central valued additive map vanishing on with ; (2) , is a derivation with for each .