Opuscula Mathematica

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

Corona theorem and isometries


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.
Cite this article as:
Krzysztof Rudol, Corona theorem and isometries, Opuscula Math. 24, no. 1 (2004), 123-131
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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