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Spectra of Toeplitz Operators and Uniform Algebras
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 |
Publisher: | Department of Mathematics, Hokkaido University |
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
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Submitter: 数学紀要登録作業用
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