Uniform algebras and projections
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- by S. J. Sidney PDF
- Proc. Amer. Math. Soc. 91 (1984), 381-382 Request permission
Abstract:
If $M$ is a closed $A$-submodule of $C\left ( X \right )$ where $A$ is a uniform algebra on $X$ which contains a separating family of unimodular functions, and if $M$ is a quotient space of some $C\left ( Y \right )$, then $M$ is an ideal in $C\left ( X \right )$. If there is an example of a uniform algebra $A$ on some $X$ such that $A \ne C\left ( X \right )$ but $A$ is complemented in $C\left ( X \right )$, then there is such an example with $A$ separable.References
- I. Glicksberg, Some uncomplemented function algebras, Trans. Amer. Math. Soc. 111 (1964), 121–137. MR 161175, DOI 10.1090/S0002-9947-1964-0161175-8
- Aleksander Pełczyński, Banach spaces of analytic functions and absolutely summing operators, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 30, American Mathematical Society, Providence, R.I., 1977. Expository lectures from the CBMS Regional Conference held at Kent State University, Kent, Ohio, July 11–16, 1976. MR 0511811
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 381-382
- MSC: Primary 46J10; Secondary 46E25
- DOI: https://doi.org/10.1090/S0002-9939-1984-0744634-4
- MathSciNet review: 744634