Fuglede’s theorem and limits of spectral operators

Hadwin, Donald W.

doi:10.1090/S0002-9939-1978-0493344-7

Fuglede’s theorem and limits of spectral operators
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by Donald W. Hadwin PDF

Proc. Amer. Math. Soc. 68 (1978), 365-368 Request permission

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

Linear operators

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