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3 results

  • INVARIANT SUBSPACES OF FINITE CODIMENSION AND UNIFORM ALGEBRAS

  • TAKAHIKO NAKAZI, TOMOKO OSAWA
  • Journal:
    Glasgow Mathematical Journal / Volume 46 / Issue 1 / January 2004
    Published online by Cambridge University Press:
    15 January 2004, pp. 117-120
    Print publication:
    January 2004
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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.