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Proceedings of the American Mathematical Society

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

 

 

Fuglede's theorem and limits of spectral operators


Author: Donald W. Hadwin
Journal: Proc. Amer. Math. Soc. 68 (1978), 365-368
MSC: Primary 46H15; Secondary 47B40
DOI: https://doi.org/10.1090/S0002-9939-1978-0493344-7
MathSciNet review: 0493344
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Abstract: Suppose K is a compact subset of the plane. A bounded sequence $ \{ {\tau _n}\} $ of unital homomorphisms from $ C(K)$ into a Banach algebra is pointwise norm convergent if and only if $ \{ {\tau _n}(\theta (z) = z)\} $ is convergent. Applications are made to norm limits of scalar type spectral operators. The proof is based on an asymptotic version of Fuglede's theorem for Banach algebras.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0493344-7
Keywords: Unital Banach algebra, unital homomorphism, scalar type spectral operator, Fuglede's theorem, spectral measure, Hilbert space, normal operator
Article copyright: © Copyright 1978 American Mathematical Society