Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0493344
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46H15, 47B40

Retrieve articles in all journals with MSC: 46H15, 47B40

Additional Information

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