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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Local operators and derivations on $ C\sp \ast$-algebras


Author: C. J. K. Batty
Journal: Trans. Amer. Math. Soc. 287 (1985), 343-352
MSC: Primary 46L55; Secondary 46L40
DOI: https://doi.org/10.1090/S0002-9947-1985-0766223-3
MathSciNet review: 766223
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Abstract: The variations on a theme of locality for a pair of operators $ (H,K)$ on a $ {C^\ast}$-algebra $ \mathfrak{A}$ are expressed algebraically. If $ K$ is a $ \ast$-derivation generating an action of $ \mathbb{R}$ on $ \mathfrak{A}$, and $ H$ is $ \ast$-linear and $ K$-local, then, under certain restrictions, $ H$ is shown to be very closely related to $ K$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0766223-3
Keywords: Local operator, derivation, $ {C^\ast}$-dynamical system, generator
Article copyright: © Copyright 1985 American Mathematical Society