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.
