PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2013 | 11 | 10 | 1843-1849
Tytuł artykułu

Thin sequences in the corona of H ∞

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 $$M(H^\infty )\backslash \mathbb{D}$$ 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.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
10
Strony
1843-1849
Opis fizyczny
Daty
wydano
2013-10-01
online
2013-07-20
Twórcy
  • Faculty of Mathematics and Informatics, Shumen University Konstantin Preslavsky, 115 Universitetska Str., 9712, Shumen, Bulgaria, stankov.d@abv.bg
  • Faculty of Mathematics and Informatics, Shumen University Konstantin Preslavsky, 115 Universitetska Str., 9712, Shumen, Bulgaria, tzonev@fmi.shu-bg.net
Bibliografia
  • [1] Axler S., Gorkin P., Sequences in the maximal ideal space of H ∞, Proc. Amer. Math. Soc., 1990, 108(3), 731–740
  • [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
  • [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]
  • [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]
  • [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]
  • [9] Izuchi K., Interpolating sequences in a homeomorphic part of H ∞, Proc. Amer. Math. Soc., 1991, 111(4), 1057–1065
  • [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]
  • [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
  • [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]
  • [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]
  • [14] Sundberg C., Wolff T.H., Interpolating sequences for QAB, Trans. Amer. Math. Soc., 1983, 276(2), 551–581
  • [15] Tzonev Tz., Thin sequences in homeomorphic part of M(H ∞), C. R. Acad. Bulgare Sci., 2009, 62(5), 533–540
  • [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
  • [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]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0281-1
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.