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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Locally closedness of unbounded derivations in $C^*$-algebras
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by Shôichi Ôta PDF
Proc. Amer. Math. Soc. 71 (1978), 222-226 Request permission

Abstract:

We study a local property of unbounded derivations in ${C^ \ast }$-algebras, introducing locally closedness for derivations. We show that a derivation is locally closed and the positive portion of the domain is closed under the square root operation if and only if for each hermitian element a in the domain the ${C^ \ast }$-subalgebra generated by a and the identity is contained in the domain.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 222-226
  • MSC: Primary 46L05
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0487474-3
  • MathSciNet review: 0487474