Corona theorem for strictly pseudoconvex domains

• Autorzy: Gwizdek Sebastian

Identyfikatory

DOI

10.7494/OpMath.2021.41.6.843

• Języki publikacji: EN

Abstrakty

EN

Nearly 60 years have passed since Lennart Carleson gave his proof of Corona Theorem for unit disc in the complex plane. It was only recently that M. Kosiek and K. Rudol obtained the first positive result for Corona Theorem in multidimensional case. Using duality methods for uniform algebras the authors proved “abstract” Corona Theorem which allowed to solve Corona Problem for a wide class of regular domains. In this paper we expand Corona Theorem to strictly pseudoconvex domains with smooth boundaries

Słowa kluczowe

EN

Banach algebra; uniform algebra; Arens product; Gleason part; band of measures; representing measures

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 6
• Strony: 843--848
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Gwizdek Sebastian

• AGH University of Science and Technology Faculty of Applied Mathematics AGH al. Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

• 1] L. Carleson, Interpolation by bounded analytic functions and the corona problem, Ann. of Math. 76 (1962), 547-559.
• [2] B.J. Cole, R.M. Range, A-measures on complex manifolds and some applications, J. Funct. Anal. 11 (1972), 393-400.
• [3] H.G. Dales, F.K. Dashiell, Jr., A.T.-M. Lau, D. Strauss, Banach Spaces of Continuous Functions as Dual Spaces, CMS Books in Mathematics/Ouvrages de Mathematiques de la SMC, Springer-Verlag, New York, 2016.
• [4] T.W. Gamelin, Uniform Algebras, Prentice Hall, Inc., Englewood Clifs, N.J. 1969.
• [5] M. Hakim, N. Sibony, Spectre de A(Q) pour les domains bornees faiblement pseudoconvexes reguliers, J. Funct. Anal. 37 (1980), 127-135.
• [6] M. Kosiek, K. Rudol, Dual algebras and A-measures, J. Funct. Spaces 2014 (2014), Article ID 364271.
• [7] M. Kosiek, K. Rudol, Corona Theorem, arXiv:2106.15683.
• [8] A. Noell, Peak points for pseudoconvex domains: a survey, J Geom. Anal. 18 (2008), 1058-1087.
• [9] H. Rossi, Holomorphical ly convex sets in several complex variables, Ann. Math. 74 (1961), 470-493.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).