Year: 1981
Type: article
Abstract: If A is a uniform algebra on X and M is a closed /4-submodule of C(X), the following are shown: that C(X)jA is not separable provided A is antisymmetric and X'\s totally disconnected and non-metrizable (in particular giving yet another proof that LTjH 00 is not separable); that C(X)/A is not reflexive unless A = C(X); and that, at least under a suitable additional hypothesis on A, C(X)/M is not reflexive if M has infinitecodimension in C(X).THEOREM.Let A be an antisymmetric uniform algebra on a compact Hausdorff space X which contains uncountably many distinct open-andclosed sets (which happens, for example, if X is totally disconnected and non-metrizable, and in any case implies non-metrizability of X).Then C(X)/A is not separable.
Author: S.J. Sidney
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1982956356