| Additive Biderivations and Centralizing Maps on Nest Algebras |
| Received:October 07, 2011 Revised:May 22, 2012 |
| Key Words:
biderivations commuting maps centralizing maps nest algebra.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11101250) and Youth Foundation of Shanxi Province (Grant No.2012021004). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.02.012 |
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