Uniform algebras and projections

Author:
S. J. Sidney

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

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Abstract | References | Similar Articles | Additional Information

Abstract: If is a closed -submodule of where is a uniform algebra on which contains a separating family of unimodular functions, and if is a quotient space of some , then is an ideal in . If there is an example of a uniform algebra on some such that but is complemented in , then there is such an example with separable.

**[1]**I. Glicksberg,*Some uncomplemented function algebras*, Trans. Amer. Math. Soc.**111**(1964), 121-137. MR**0161175 (28:4383)****[2]**A. Pełczyński,*Banach spaces of analytic functions and absolutely summing operators*, CBMS Regional Conf. Ser. Math., No. 30, Amer. Math. Soc., Providence, R.I., 1977. MR**0511811 (58:23526)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1984-0744634-4

Keywords:
Uniform algebra,
projection,
complemented

Article copyright:
© Copyright 1984
American Mathematical Society