A general Hoffman-Wermer theorem for algebras of operator fields
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- by D. C. Taylor PDF
- Proc. Amer. Math. Soc. 52 (1975), 212-216 Request permission
Abstract:
Let $A$ be a closed separating subalgebra of $C(T)$ that contains the identity. It is known that $\operatorname {Re} A$ is uniformly closed only if $A = C(T)$. In this note it is shown that this property characterizes all maximal full algebras of operator fields and not just $C(T)$.References
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars Éditeur, Paris, 1969 (French). Deuxième édition. MR 0246136
- J. M. G. Fell, The structure of algebras of operator fields, Acta Math. 106 (1961), 233–280. MR 164248, DOI 10.1007/BF02545788
- Kenneth Hoffman and John Wermer, A characterization of $C(X)$, Pacific J. Math. 12 (1962), 941–944. MR 150324
- Donald Curtis Taylor, Interpolation in algebras of operator fields, J. Functional Analysis 10 (1972), 159–190. MR 0377528, DOI 10.1016/0022-1236(72)90047-x
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 212-216
- MSC: Primary 46L99
- DOI: https://doi.org/10.1090/S0002-9939-1975-0385594-2
- MathSciNet review: 0385594