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Proceedings of the American Mathematical Society

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



On the normal spectrum of a subnormal operator

Authors: J. W. Bunce and J. A. Deddens
Journal: Proc. Amer. Math. Soc. 63 (1977), 107-110
MSC: Primary 47B20; Secondary 46L05
MathSciNet review: 0435912
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Abstract: In this note we present a new characterization for subnormality which is purely $ {C^ \ast }$-algebraic. We also establish an intrinsic characterization of the normal spectrum for a subnormal operator, which enables us to prove that $ {\sigma _ \bot }(\pi (S)) \subseteq {\sigma _ \bot }(S)$ for any $ ^ \ast $-representation $ \pi $.

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Keywords: Subnormal operator, normal spectrum, $ {C^ \ast }$-algebra
Article copyright: © Copyright 1977 American Mathematical Society

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