On derivations annihilating a maximal abelian subalgebra

Author:
Geoffrey L. Price

Journal:
Trans. Amer. Math. Soc. **290** (1985), 843-850

MSC:
Primary 46L40; Secondary 46L55

DOI:
https://doi.org/10.1090/S0002-9947-1985-0792832-1

MathSciNet review:
792832

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an -algebra, and let be a closed -derivation which annihilates the maximal abelian subalgebra of diagonal elements of . Then we show that generates an approximately inner -dynamics on , and that is a commutative -derivation. Any two closed -derivations vanishing on are shown to be strongly commuting. More generally, if is a semiderivation on which vanishes on , we prove that is a generator of a semigroup of strongly positive contractions of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1985-0792832-1

Keywords:
Derivation,
-algebra,
maximal abelian subalgebra,
approximately inner,
generator

Article copyright:
© Copyright 1985
American Mathematical Society