|
|
|
|
Список литературы
|
|
| |
| 1. |
Bass H., “$K$-theory and stable algebra”, Inst. Hautes Etudes Sci. Publ. Math., 22 (1964), 5–60 |
| 2. |
Behrens M., “The corona conjecture for a class of infinitely connected domains”, Bull. Amer. Math. Soc., 76:2 (1970), 387–391 |
| 3. |
Brudnyi A., “Topology of the maximal ideal space of $H^\infty$”, J. Funct. Anal., 189:1 (2002), 21–52 |
| 4. |
Brudnyi A., “Projections in the space $H^\infty$ and the corona theorem for subdomains of coverings of finite bordered Riemann surfaces”, Ark. Mat., 42 (2004), 31–59 |
| 5. |
Brudnyi A., “Grauert- and Lax-Halmos-type theorems and extension of matrices with entries in $H^\infty$”, J. Funct. Anal., 206 (2004), 87–108 |
| 6. |
Brudnyi A., “On the completion problem for algebra $H^\infty$”, J. Funct. Anal., 266:7 (2014), 4293–4313 |
| 7. |
Brudnyi A., “Topology of the maximal ideal space of $H^\infty$ revisited”, Adv. Math., 299 (2016), 931–939 |
| 8. |
Brudnyi A., “Banach-valued holomorphic functions on the maximal ideal space of $H^\infty$”, Invent. Math., 193:1 (2013), 187–227 |
| 9. |
Brudnyi A., “Oka principle on the maximal ideal space of $H^\infty$”, Алгебра и анализ, 31:5 (2019), 24–89 |
| 10. |
Brudnyi A., “Projective freeness of algebras of bounded holomorphic functions on infinitely connected domains”, Алгебра и анализ, 33:4 (2021), 49–65 |
| 11. |
Brudnyi A., “Structure of the maximal ideal space of $H^\infty$ on the countable disjoint union of open disks”, Алгебра и анализ, 32:6 (2020), 58–71 |
| 12. |
Brudnyi A., “Dense stable rank and Runge type approximation theorems for $H^\infty$ maps”, J. Aust. Math. Soc. |
| 13. |
Brudnyi A., “On stable rank of $H^\infty$ on coverings of bordered Riemann surfaces”, Rev. Mat. Iberoam. |
| 14. |
Brudnyi A., “On homotopy invariants of tensor products of Banach algebras”, Integral Equations Operator Theory, 92:2 (2020), 19, 14 pp. |
| 15. |
Carleson L., “Interpolations by bounded analytic functions and the corona theorem”, Ann. Math. (2), 76 (1962), 547–559 |
| 16. |
Corach G., Suárez F. D., “Extension problems and stable rank in commutative Banach algebras”, Topology Appl., 21 (1985), 1–8 |
| 17. |
Douady A., “Un espace de Banach dont le groupe linéaire n'est pas connexe”, Indag. Math., 27 (1965), 787–789 |
| 18. |
Garnett J. B., Bounded analytic functions, Pure Appl. Math., 96, Acad. Press, New York, 1981 |
| 19. |
Hoffman K., “Bounded analytic functions and Gleason parts”, Ann. Math. (2), 86 (1967), 74–111 |
| 20. |
Hoffman K., “Analytic functions and logmodular Banach algebras”, Acta Math., 108 (1962), 271–317 |
| 21. |
Husemoller D., Fibre bundles, Grad. Texts in Math., 20, Springer-Verlag, New York, 1994 |
| 22. |
Lindenstrauss J., “On complemented subspaces of $m$”, Israel J. Math., 5 (1967), 153–156 |
| 23. |
Митягин Б. С., “Гомотопическая структура линейной группы банахова пространства”, Успехи мат. наук, 25:5 (1970), 63–106 |
| 24. |
Mortini R., Sasane A., Wick B. D., “The Corona theorem and stable rank for the algebra $\mathbb{C} + BH^\infty$”, Houston J. Math., 36:1 (2010), 289–302 |
| 25. |
Nikolski N. K., Operators, functions, and systems: an easy reading, v. 1, Math. Surveys Monogr., 92, Hardy, Hankel, and Toeplitz, Amer. Math. Soc., Providence, RI, 2002 |
| 26. |
Pełczyński A., “Projections in certain Banach spaces”, Studia Math., 19 (1960), 209–228 |
| 27. |
Suárez D., “Čech cohomology and covering dimension for the $H^\infty$ maximal ideal space”, J. Funct. Anal., 123:2 (1994), 233–263 |
| 28. |
Suárez D., “Trivial Gleason parts and the topological stable rank of $H^\infty$”, Amer. J. Math., 118:4 (1996), 879–904 |
| 29. |
Stout E. L., “Bounded holomorphic functions on finite Riemann surfaces”, Trans. Amer. Math. Soc., 120 (1965), 255–285 |
| 30. |
Treil S., “The stable rank of $H^\infty$ is equal to one”, J. Funct. Anal., 109 (1992), 130–154 |