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Essentially commutative C*-algebras with essential spectrum homeomorphic to S2n−1

Part of: Special classes of linear operators General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Kunyu Guo
Kunyu Guo
Affiliation:
Department of Mathematics Fudan UniversityShanghai, 200433 P.R.China e-mail: kyguo@fudan.edu.cn
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Abstract

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This paper gives a complete classification of essentially commutative C*-algebras whose essential spectrum is homeomorphic to S2n−1 by their characteristic numbers. Let 1, 2 be such two C*-algebras; then they are C*-isomorphic if and only if they have the same n-th characteristic number. Furthermore, let γn() = m then is C*-isomorphic to C*(Mzl, …, Mzn) if m = 0, is C*-isomorphic C*(Tz1, …, Tzn−1, Tznm) if m ≠ 0. Some examples are given to show applications of the classfication theorem. We finally remark that the proof of the theorem depends on a construction of a complete system of representatives of Ext(S2n−1).

Keywords

characteristic numbersessential spectrumextensionsmapping degree.

MSC classification

Secondary: 47A53: (Semi-) Fredholm operators; index theories 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 2 , April 2001 , pp. 199 - 210
Copyright
Copyright © Australian Mathematical Society 2001

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