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Proceedings of the American Mathematical Society

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

 
 

 

Locally closedness of unbounded derivations in $C^*$-algebras


Author: Shôichi Ôta
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
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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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Keywords: <!– MATH ${C^ \ast }$ –> <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${C^ \ast }$">-algebras, unbounded derivation, closability, locally closedness
Article copyright: © Copyright 1978 American Mathematical Society