Geodesic
Estimates in the problem of ideals in the algebra $H^\infty$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 44, Tome 447 (2016), pp. 66-74 
I. K. Zlotnikov. Estimates in the problem of ideals in the algebra $H^\infty$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 44, Tome 447 (2016), pp. 66-74. http://geodesic.mathdoc.fr/item/ZNSL_2016_447_a4/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

By using the fixed-point approach due to D. Rutsky, the problem of ideals in $H^\infty$ is solved for “data sequences” in $H^\infty(l^1)$ (instead of $H^\infty(l^2)$ in the traditional setting).

[1] S. V. Kislyakov, “Teorema o korone i interpolyatsiya”, Algebra i analiz, 27:5 (2015), 69–80

[2] D. Rutsky, Corona problem with data in ideal spaces of sequences, Preprint, arXiv: 1507.03798

[3] V. A. Tolokonnikov, “Otsenki v teoreme Karlesona o korone, idealy algebry $H^\infty$, zadacha Sekefalvi-Nadya”, Zap. nauchn. semin. LOMI, 113, 1981, 178–198 | MR | Zbl

[4] U. Cegrell, “A generalization of the corona theorem in the unit disc”, Math. Z., 203 (1990), 255–261 | DOI | MR | Zbl

[5] S. Treil, “The problem of ideals of $H^\infty$: beyond the exponent 3/2”, J. Funct. Anal., 253:1 (2007), 220–240 | DOI | MR | Zbl

[6] L. Rubel, A. Shields, “The space of bounded analytic functions on a region”, Annales de l'institut Fourier, 16:1 (1966), 235–277 | DOI | MR | Zbl

[7] C. V. Kislyakov, D. V. Rutskii, “Neskolko zamechanii k teoreme o korone”, Algebra i analiz, 24:2 (2012), 171–191 | MR | Zbl