Certain properties of derivations

Author:
Mark Spivack

Journal:
Proc. Amer. Math. Soc. **99** (1987), 712-718

MSC:
Primary 47D25

MathSciNet review:
877045

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Abstract: We consider two properties of implemented derivations on operator algebras, and give applications. One provides a simple test and leads to examples of nonimplemented derivations on commutative algebras. The other is stronger and yields a necessary and sufficient condition for derivations on to be implemented, where is a Hilbert space and is a projection on . Any algebra on has an extension to an algebra acting on containing such an algebra. We show that any derivation on an algebra is implemented if and only if has a bounded strongly continuous extension to . If so we can construct an implementing operator explicitly.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1987-0877045-4

Article copyright:
© Copyright 1987
American Mathematical Society