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Abstract:

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.

Registro:

Documento: Artículo
Título:Homeomorphic analytic maps into the maximal ideal space of H∞
Autor:Suárez, D.
Filiación:Departamento de Matemática, Fac. Cs. Exact. y Nat. UBA, Ciudad Universitaria, (1428) Núñez, Argentina
Año:1999
Volumen:51
Número:1
Página de inicio:147
Página de fin:163
DOI: http://dx.doi.org/10.4153/CJM-1999-009-5
Título revista:Canadian Journal of Mathematics
Título revista abreviado:Can. J. Math.
ISSN:0008414X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0008414X_v51_n1_p147_Suarez

Referencias:

  • Budde, P., (1982) Support Sets and Gleason Parts of M(h∞), , Thesis, Univ. of California, Berkeley
  • Carleson, L., Interpolations by bounded analytic functions and the corona theorem (1962) Ann. of Math., 76, pp. 547-559
  • Garnett, J.B., (1981) Bounded Analytic Functions, , Academic Press, New York
  • Gorkin, P., Gleason parts and COP (1989) J. Funct. Anal., 83, pp. 44-49
  • Gorkin, P., Lingenberg, H.M., Mortini, R., Homeomorphic disks in the spectrum of H∞ (1990) Indiana Univ. Math. J., 39, pp. 961-983
  • Gorkin, P., Mortini, R., Alling's conjecture on closed prime ideals in H∞ (1997) J. Funct. Anal., 148, pp. 185-190
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  • Izuchi, K., Spreading Blaschke Products and Homeomorphic Parts, , Preprint
  • Kelley, J.L., (1955) General Topology, , Van Nostrand-Reinhold, Princeton, NJ
  • Marshall, D.E., Blaschke products generate H∞ (1976) Bull. Amer. Math. Soc., 82, pp. 494-496
  • Mortini, R., Gleason parts and prime ideals in H∞ (1994) Linear and Complex Analysis Problem Book, Lecture Notes in Math., 1573, pp. 136-138
  • Suárez, D., Čech cohomology and covering dimension for the H∞ maximal ideal space (1994) J. Funct. Anal., 123, pp. 233-263
  • Trivial Gleason parts and the topological stable rank of H∞ (1996) Amer. J. Math., 118, pp. 879-904
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Citas:

---------- APA ----------
(1999) . Homeomorphic analytic maps into the maximal ideal space of H∞. Canadian Journal of Mathematics, 51(1), 147-163.
http://dx.doi.org/10.4153/CJM-1999-009-5
---------- CHICAGO ----------
Suárez, D. "Homeomorphic analytic maps into the maximal ideal space of H∞" . Canadian Journal of Mathematics 51, no. 1 (1999) : 147-163.
http://dx.doi.org/10.4153/CJM-1999-009-5
---------- MLA ----------
Suárez, D. "Homeomorphic analytic maps into the maximal ideal space of H∞" . Canadian Journal of Mathematics, vol. 51, no. 1, 1999, pp. 147-163.
http://dx.doi.org/10.4153/CJM-1999-009-5
---------- VANCOUVER ----------
Suárez, D. Homeomorphic analytic maps into the maximal ideal space of H∞. Can. J. Math. 1999;51(1):147-163.
http://dx.doi.org/10.4153/CJM-1999-009-5