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| CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONSOF NEST ALGEBRAS ON BANACH SPACES |
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Citation： |
Han Deguang.CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONSOF NEST ALGEBRAS ON BANACH SPACES[J].Chinese Annals of Mathematics B,1996,17(2):227~236 |
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Net amount： 930 |
Authors： |
Han Deguang; |
Foundation： |
Project supported by the National Natural Science
Foundation of China |
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| Abstract： |
This paper discusses the problem concerning the continuity and
linearity of additive derivation of nest algebras on normed
spaces. It is proved that every linear derivation of a nest
algebra alg$\Cal N$ is continuous provided that one of the
following conditions is satisfied: (1) $0_+\supset 0.$ (2)
$X_-\subset X.$ (3) there exists a non-trivial idempotent $p$ in
alg$\Cal N$ such that the range of $p$ belongs to $\Cal N$. It is
also proved that every additive derivation of a nest algebra is
automatically linear if the underlying normed space is infinite
dimemnsional. |
Keywords： |
Nest algebra, Derivation, Continuity, Linearity,
Banach space |
Classification： |
47D25, 47B47 |
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