Geodesic
Homeomorphic Analytic Maps into the Maximal Ideal Space of H ∞
Canadian journal of mathematics, Tome 51 (1999) no. 1, pp. 147-163

Voir la notice de l'article provenant de la source Cambridge University Press

Let $m$ be a point of the maximal ideal space of ${{H}^{\infty }}$ with nontrivial Gleason part $P\left( m \right)$ . If ${{L}_{m}}\,:\,\text{D}\,\to \,\text{P(m)}$ is the Hoffman map, we show that ${{H}^{\infty }}\,\circ \,{{L}_{m}}$ is a closed subalgebra of ${{H}^{\infty }}$ . We characterize the points $m$ for which ${{L}_{m}}$ is a homeomorphism in terms of interpolating sequences, and we show that in this case ${{H}^{\infty }}\,\circ \,{{L}_{m}}$ coincides with ${{H}^{\infty }}$ . Also, if ${{I}_{m}}$ is the ideal of functions in ${{H}^{\infty }}$ that identically vanish on $P\left( m \right)$ , we estimate the distance of any $f\,\in \,{{H}^{\infty }}\,\text{to}\,{{I}_{m}}$ .
DOI : 10.4153/CJM-1999-009-5
Mots-clés : 30H05, 46J20 
Suárez, Daniel. Homeomorphic Analytic Maps into the Maximal Ideal Space of H ∞. Canadian journal of mathematics, Tome 51 (1999) no. 1, pp. 147-163. doi: 10.4153/CJM-1999-009-5
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