In this paper we consider several conditions for sequences of points in M(H ∞) and establish relations between them. We show that every interpolating sequence for QA of nontrivial points in the corona of H ∞ is a thin sequence for H ∞, which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of H ∞ necessarily satisfy the same condition.
@article{bwmeta1.element.doi-10_2478_s11533-013-0281-1,
author = {Dimcho Stankov and Tzonio Tzonev},
title = {Thin sequences in the corona of H $\infty$},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1843-1849},
zbl = {1278.30056},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0281-1}
}
Dimcho Stankov; Tzonio Tzonev. Thin sequences in the corona of H ∞. Open Mathematics, Tome 11 (2013) pp. 1843-1849. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0281-1/
[1] Axler S., Gorkin P., Sequences in the maximal ideal space of H ∞, Proc. Amer. Math. Soc., 1990, 108(3), 731–740 | Zbl 0703.46037
[2] Carleson L., An interpolation problem for bounded analytic functions, Amer. J. Math., 1958, 80(4), 921–930 http://dx.doi.org/10.2307/2372840[Crossref]
[3] Garnett J.B., Bounded Analytic Functions, Grad. Texts in Math., 236, Springer, New York, 2007 | Zbl 1106.30001
[4] Gorkin P., Lingenberg H.-M., Mortini R., Homeomorphic disks in the spectrum of H ∞, Indiana Univ. Math. J., 1990, 39(4), 961–983 http://dx.doi.org/10.1512/iumj.1990.39.39046[Crossref]
[5] Gorkin P., Mortini R., Asymptotic interpolating sequences in uniform algebras, J. London Math. Soc., 2003, 67(2), 481–498 http://dx.doi.org/10.1112/S0024610702004039[Crossref] | Zbl 1054.46036
[6] Gorkin P., Mortini R., Universal Blaschke products, Math. Proc. Cambridge Phil. Soc., 2004, 136(1), 175–184 http://dx.doi.org/10.1017/S0305004103007023[Crossref]
[7] Hedenmalm H., Thin interpolating sequences and three algebras of bounded functions, Proc. Amer. Math. Soc., 1987, 99(3), 489–495 http://dx.doi.org/10.1090/S0002-9939-1987-0875386-8[Crossref] | Zbl 0617.46059
[8] Hoffman K., Bounded analytic functions and Gleason parts, Ann. of Math., 1967, 86(1), 74–111 http://dx.doi.org/10.2307/1970361[Crossref] | Zbl 0192.48302
[9] Izuchi K., Interpolating sequences in a homeomorphic part of H ∞, Proc. Amer. Math. Soc., 1991, 111(4), 1057–1065 | Zbl 0726.46034
[10] Izuchi K., Interpolating sequences in the maximal ideal space of H ∞, J. Math. Soc. Japan, 1991, 43(4), 721–731 http://dx.doi.org/10.2969/jmsj/04340721[Crossref] | Zbl 0754.46037
[11] Izuchi K., Interpolating sequences in the maximal ideal space of H ∞. II, In: Operator Theory, Advances and Applications, Sapporo, 1991, Oper. Theory Adv. Appl., 59, Birkhäuser, Basel, 1992, 221–233 | Zbl 0799.46062
[12] Mortini R., Interpolating sequences in the spectrum of H ∞. I, Proc. Amer. Math. Soc., 2000, 128(6), 1703–1710 http://dx.doi.org/10.1090/S0002-9939-99-05161-8[Crossref] | Zbl 0948.46037
[13] Mortini R., Thin interpolating sequences in the disk, Arch. Math. (Basel), 2009, 92(5), 504–518 http://dx.doi.org/10.1007/s00013-009-3057-x[WoS][Crossref] | Zbl 1179.30058
[14] Sundberg C., Wolff T.H., Interpolating sequences for QAB, Trans. Amer. Math. Soc., 1983, 276(2), 551–581 | Zbl 0536.30025
[15] Tzonev Tz., Thin sequences in homeomorphic part of M(H ∞), C. R. Acad. Bulgare Sci., 2009, 62(5), 533–540 | Zbl 1199.30275
[16] Tzonev Tz.G., Stankov D.K., Sufficient conditions for thinness of sequences in M(H ∞), C. R. Acad. Bulgare Sci., 2000, 53(1), 9–12 | Zbl 0959.46040
[17] Wolff T., Two algebras of bounded functions, Duke Math. J., 1982, 49(2), 321–328 http://dx.doi.org/10.1215/S0012-7094-82-04920-1[Crossref]