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INVARIANT SUBSPACES OF FINITE CODIMENSION AND UNIFORM ALGEBRAS

Published online by Cambridge University Press:  15 January 2004

TAKAHIKO NAKAZI
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan e-mail: [email protected]
TOMOKO OSAWA
Affiliation:
Mathematical and Scientific Subjects, Asahikawa National College of Technology, Asahikwa 071-8142, Japan e-mail: [email protected]
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Abstract

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Let $A$ be a uniform algebra on a compact Hausdorff space $X$ and $m$ a probability measure on $X$. Let $H^p(m)$ be the norm closure of $A$ in $L^p(m)$ with $1 \le p < \infty$ and $H^\infty(m)$ the weak $\ast$ closure of $A$ in $L^\infty(m)$. In this paper, we describe a closed ideal of $A$ and exhibit a closed invariant subspace of $H^p(m)$ for $A$ that is of finite codimension.

Keywords

Type
Research Article
Copyright
2004 Glasgow Mathematical Journal Trust