Fuglede’s theorem and limits of spectral operators
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- by Donald W. Hadwin
- Proc. Amer. Math. Soc. 68 (1978), 365-368
- DOI: https://doi.org/10.1090/S0002-9939-1978-0493344-7
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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.References
- N. Dunford and J. T. Schwartz, Linear operators, III, Interscience, New York, 1971.
- Bent Fuglede, A commutativity theorem for normal operators, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 35–40. MR 32944, DOI 10.1073/pnas.36.1.35
- Donald W. Hadwin, An asymptotic double commutant theorem for $C^{\ast }$-algebras, Trans. Amer. Math. Soc. 244 (1978), 273–297. MR 506620, DOI 10.1090/S0002-9947-1978-0506620-0
- Robert Moore, An asymptotic Fuglede theorem, Proc. Amer. Math. Soc. 50 (1975), 138–142. MR 370247, DOI 10.1090/S0002-9939-1975-0370247-7
- C. R. Putnam, On normal operators in Hilbert space, Amer. J. Math. 73 (1951), 357–362. MR 40585, DOI 10.2307/2372180
- M. Rosenblum, On a theorem of Fuglede and Putnam, J. London Math. Soc. 33 (1958), 376–377. MR 99598, DOI 10.1112/jlms/s1-33.3.376
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- 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