Additive Biderivations and Centralizing Maps on Nest Algebras
Received:October 07, 2011  Revised:May 22, 2012
Key Word: biderivations   commuting maps   centralizing maps   nest algebra.
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11101250) and Youth Foundation of Shanxi Province (Grant No.2012021004).
 Author Name Affiliation Xiaofei QI Department of Mathematics, Shanxi University, Shanxi 030006, P. R. China
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Let $\mathcal N$ be a nest on a Banach space $X$, and Alg$\mathcal N$ be the associated nest algebra. It is shown that, if there exists a non-trivial element $N$ in $\mathcal N$ which is complemented in $X$ and $\dim N\not=1$, then every additive biderivation from Alg$\mathcal N$ into itself is an inner biderivation. Based on this result, we give characterizations of centralizing (commuting) maps, cocentralizing derivations, and cocommuting generalized derivations on nest algebras.