Local derivations of nest algebras

Authors:
De Guang Han and Shu Yun Wei

Journal:
Proc. Amer. Math. Soc. **123** (1995), 3095-3100

MSC:
Primary 47D25; Secondary 47B47

DOI:
https://doi.org/10.1090/S0002-9939-1995-1246521-1

MathSciNet review:
1246521

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Abstract: Let *X* be an arbitrary reflexive Banach space, and let be a nest on *X*. Denote by the set of all derivations from into . For , we set . We also write . Finally, for define . In this paper we prove that a sufficient condition for to be (topologically) algebraically reflexive is that for all and for all , there exist and , such that and . In particular, we prove that this condition automatically holds for nests acting on finite-dimensional Banach spaces.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1246521-1

Keywords:
Local derivation,
nest algebras

Article copyright:
© Copyright 1995
American Mathematical Society