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Homeomorphic Analytic Maps into the Maximal Ideal Space of $H^\infty$

 Printed: Feb 1999
  • Daniel Suárez
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Let $m$ be a point of the maximal ideal space of $\papa$ with nontrivial Gleason part $P(m)$. If $L_m \colon \disc \rr P(m)$ is the Hoffman map, we show that $\papa \circ L_m$ is a closed subalgebra of $\papa$. We characterize the points $m$ for which $L_m$ is a homeomorphism in terms of interpolating sequences, and we show that in this case $\papa \circ L_m$ coincides with $\papa$. Also, if $I_m$ is the ideal of functions in $\papa$ that identically vanish on $P(m)$, we estimate the distance of any $f\in \papa$ to $I_m$.
MSC Classifications: 30H05, 46J20 show english descriptions Bounded analytic functions
Ideals, maximal ideals, boundaries
30H05 - Bounded analytic functions
46J20 - Ideals, maximal ideals, boundaries

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