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Spectra of Toeplitz Operators and Uniform Algebras

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83726

Title: Spectra of Toeplitz Operators and Uniform Algebras
Authors: Nakazi, T. Browse this author
Osawa, T. Browse this author
Keywords: Toeplitz operator
uniform algebra
spectrum
convex­hull
index
Issue Date: Jan-2003
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 581
Start Page: 1
End Page: 9
Abstract: Let A be a uniform algebra on X and P a set of all probability measures on X. For each µ in P, H2 (µ) is the closure of A in L2 (µ) and Tt is a Toeplitz operator on H2 (µ) for a continuous function cf> on X. In this paper we study the invertibility and the spectrum of Tip = L EB Tt. We show that if Tip is invertible then the index of cf> is zero and if the converse is true for an arbitrary continuous function cf> then A is a Dirichlet algebra on X. Moreover we study the spectrum of Tip.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69330
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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