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A general Hoffman-Wermer theorem for algebras of operator fields


Author: D. C. Taylor
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
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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 [Enhancements On Off] (What's this?)

  • [1] J. Dixmier, Les $ {C^{\ast}}$-algèbres et leurs représentations, Cahiers Scientifiques, fasc. 29, Gauthier-Villars, Paris, 1969. MR 39 #7442. MR 0246136 (39:7442)
  • [2] J. Fell, The structure of algebras of operator fields, Acta Math. 106 (1961), 233-280. MR 29 #1547. MR 0164248 (29:1547)
  • [3] K. Hoffman and J. Wermer, A characterization of $ C(X)$, Pacific J. Math. 12 (1962), 941-944. MR 27 #325. MR 0150324 (27:325)
  • [4] D. Taylor, Interpolation in algebras of operator fields, J. Functional Analysis 10 (1972), 159-190. MR 0377528 (51:13700)

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DOI: https://doi.org/10.1090/S0002-9939-1975-0385594-2
Article copyright: © Copyright 1975 American Mathematical Society

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