Homeomorphic analytic maps into the maximal ideal space of H∞
Let m be a point of the maximal ideal space of H∞ with nontrivial Gleason part P(m). If Lm : double-struck D sign → P(m) is the Huffman map, we show that H∞ ○ Lm is a closed subalgebra of H∞. We characterize the points m for which Lm is a homeomorphism in terms of interpolating sequences, and we sho...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0008414X_v51_n1_p147_Suarez |
| Aporte de: |
| Sumario: | Let m be a point of the maximal ideal space of H∞ with nontrivial Gleason part P(m). If Lm : double-struck D sign → P(m) is the Huffman map, we show that H∞ ○ Lm is a closed subalgebra of H∞. We characterize the points m for which Lm is a homeomorphism in terms of interpolating sequences, and we show that in this case H∞ ○ Lm coincides with H∞. Also, if Im is the ideal of functions in H∞ that identically vanish on P(m), we estimate the distance of any f ∈ H∞ to Im. |
|---|