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Proceedings of the American Mathematical Society

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The norm of a derivation in a $ W\sp{\ast} $-algebra


Author: László Zsidó
Journal: Proc. Amer. Math. Soc. 38 (1973), 147-150
MSC: Primary 46L10
MathSciNet review: 0326412
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Abstract: The norm of an inner derivation $ {\delta _a}$ of a (nonnecessary separable) $ {W^ \ast }$-algebra $ M$ is shown to satisfy

$\displaystyle \vert\vert{\delta _a}\vert\vert = 2\inf \{ \vert\vert a - z\vert\vert;z \in Z,\;{\text{the center of}\; M\} ,}$

and some related results are obtained.

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DOI: https://doi.org/10.1090/S0002-9939-1973-0326412-6
Keywords: $ {W^ \ast }$-algebra, hyperstonean space, derivation
Article copyright: © Copyright 1973 American Mathematical Society