Corona Theorem and isometries

• Autorzy: Rudol K.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Hardy classes; Taylor's joint spectra; cluster sets

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2004
• Tom: Vol. 24, no. 1
• Strony: 123--131
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Rudol K.

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland,

Bibliografia

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• [15] Rudol K.: Spectra of pairs of isometries. (to appear).
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• [19] Wolff R.: Spectra of analytic Toeplitz tuples on Hardy spaces. Bull. London Math. Soc. 29 (1997), 65-72.