Geodesic
Structure of the maximal ideal space of $H^\infty$ on the countable disjoint union of open disks
Algebra i analiz, Tome 32 (2020) no. 6, pp. 58-71.

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The maximal ideal space of the algebra of bounded holomorphic functions on the countable disjoint union of open unit disks $\mathbb{D}\subset\mathbb{C}$ is studied from a topological point of view. The results are similar to those for the maximal ideal space of the algebra $H^\infty(\mathbb{D})$.
Keywords: maximal ideal space of $H^\infty(\mathbb{D}\times\mathbb{N})$, interpolating sequence, Blaschke product, Gleason part, analytic disk, covering dimension, cohomology, Freudenthal compactification. 
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A. Brudnyi. Structure of the maximal ideal space of $H^\infty$ on the countable disjoint union of open disks. Algebra i analiz, Tome 32 (2020) no. 6, pp. 58-71. http://geodesic.mathdoc.fr/item/AA_2020_32_6_a2/

[1] Behrens M., “The corona conjecture for a class of infinitely connected domains”, Bull. Amer. Math. Soc., 76:2 (1970), 387–391 | DOI | MR | Zbl

[2] Brudnyi A., “Topology of the maximal ideal space of $H^{\infty}$”, J. Funct. Anal., 189:1 (2002), 21–52 | DOI | MR | Zbl

[3] Brudnyi A., “Topology of the maximal ideal space of $H^\infty$ revisited”, Adv. Math., 299 (2016), 931–939 | DOI | MR | Zbl

[4] Brudnyi A., “Banach-valued holomorphic functions on the maximal ideal space of $H^\infty$”, Invent. Math., 193 (2013), 187–227 | DOI | MR | Zbl

[5] Brudnyi A., “Holomorphic Banach vector bundles on the maximal ideal space of $H^\infty$ and the operator corona problem of Sz.-Nagy”, Adv. Math., 232 (2013), 121–141 | DOI | MR | Zbl

[6] Brudnyi A., “Oka principle on the maximal ideal space of $H^\infty$”, Algebra i analiz, 31:5 (2019), 24–89 | MR

[7] Brudnyi A., Projective freeness of algebras of bounded holomorphic functions on infinitely connected domains, arXiv: 1905.01532

[8] Brudnyi A., Dense stable rank and Runge type approximation theorems for $H^\infty$ maps, arXiv: 2006.04179

[9] Carleson L., “Interpolations by bounded analytic functions and the corona theorem”, Ann. of Math. (2), 76 (1962), 547–559 | DOI | MR | Zbl

[10] Garnett J. B., Bounded analytic functions, Pure Appl. Math., 96, Acad. Press, New York, 1981 | MR | Zbl

[11] Hoffman K., “Bounded analytic functions and Gleason parts”, Ann. of Math. (2), 86 (1967), 74–111 | DOI | MR | Zbl

[12] Hoffman K., “Analytic functions and logmodular Banach algebras”, Acta Math., 108 (1962), 271–317 | DOI | MR | Zbl

[13] Hu S.-T., “Mappings of a normal space into an absolute neighborhood retract”, Trans. Amer. Math. Soc., 64 (1948), 336–358 | DOI | MR | Zbl

[14] Husemoller D., Fibre bundles, Grad. Texts in Math., 20, Springer-Verlag, New York, 1994 | DOI | MR

[15] Nikolskii N. K., Treatise on the shift operator. Spectral function theory, Grundlehren Math. Wiss., 273, Springer-Verlag, Berlin, 1986 | DOI | MR | Zbl

[16] Suárez D., “Čech cohomology and covering dimension for the $H^\infty$ maximal ideal space”, J. Funct. Anal., 123:2 (1994), 233–263 | DOI | MR

[17] Suárez D., “Trivial Gleason parts and the topological stable rank of $H^\infty$”, Amer. J. Math., 118:4 (1996), 879–904 | DOI | MR

[18] Taylor J. L., “Topological invariants of the maximal ideal space of a Banach algebra”, Adv. Math., 19:2 (1976), 149–206 | DOI | MR | Zbl

[19] Tolokonnikov V., “Extension problem to an invertible matrix”, Proc. Amer. Math. Soc., 117:4 (1993), 1023–1030 | DOI | MR | Zbl