Opuscula Mathematica
Opuscula Math. 41, no. 6 (2021), 843-848

Corona theorem for strictly pseudoconvex domains

Sebastian Gwizdek
Abstract. 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.
Keywords: Corona theorem, Banach algebra, uniform algebra, Arens product, Gleason part, band of measures, representing measure.
Mathematics Subject Classification: 30H80, 32A38, 32A65, 32A70, 46J10, 46J15, 46J20.
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About the authors ▼
Sebastian Gwizdek
https://orcid.org/0000-0002-9149-8507
AGH University of Science and Technology, Faculty of Applied Mathematics AGH, al. Mickiewicza 30, 30-059 Kraków, Poland
About the article ▼
Communicated by P.A. Cojuhari.
Received: 2021-07-01.
Revised: 2021-08-12.
Accepted: 2021-08-13.
Published online: 2021-11-29.
Cite this article as ▼
Sebastian Gwizdek, Corona theorem for strictly pseudoconvex domains, Opuscula Math. 41, no. 6 (2021), 843-848, https://doi.org/10.7494/OpMath.2021.41.6.843.
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