Opuscula Math. 24, no. 1 (2004), 123-131

Opuscula Mathematica

Corona theorem and isometries

Krzysztof Rudol

Abstract. The aim of this note is to discuss a new operator theory approach to Corona Problem. An equivalent operator problem invariant under unitary equivalence is stated. The related condition involves certain joint spectra of commuting subnormal operators. A special case leading to isometries is studied. As a result one obtains a relatively short proof of Corona Theorem for a wide class of domains in the plane, where Marshall's Theorem on the approximation by inner functions holds.

Keywords: Hardy classes, Taylor's joint spectra, cluster sets.

Mathematics Subject Classification: 47B20, 46J15, 32E25.

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Krzysztof Rudol, Corona theorem and isometries, Opuscula Math. 24, no. 1 (2004), 123-131

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