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

Opuscula Mathematica

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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  • Communicated by P.A. Cojuhari.
  • Received: 2021-07-01.
  • Revised: 2021-08-12.
  • Accepted: 2021-08-13.
  • Published online: 2021-11-29.
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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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