Journal article
C-ALGEBRAS OF SINGULAR INTEGRAL OPERATORS AND TOEPLITZ OPERATORS ASSOCIATED WITH n-DIMENSIONAL FLOWS
International journal of mathematics, Vol.3(4), pp.525-579
08/1992
DOI: 10.1142/S0129167X92000254
Abstract
For a given covariant representation π of an n-dimensional dynamical system (X, R n, α), we study the C*-algebras [Formula: see text] of abstract singular integral opertors and Toeplitz operators generated by π(C(X)) and Hilbert transforms corresponding to n linearly independent directions. Such an algebra has a chain of ideals [Formula: see text]. We compute all [Formula: see text] and show that for 0≤k≤n−1 each of these quotients is the direct sum of C*-algebras which can be thought of as [Formula: see text] for flows of lower dimensions. The ideal structure of [Formula: see text] is carefully studied. We also determine precisely when [Formula: see text] is a C*-algebra of type I.
Details
- Title: Subtitle
- C-ALGEBRAS OF SINGULAR INTEGRAL OPERATORS AND TOEPLITZ OPERATORS ASSOCIATED WITH n-DIMENSIONAL FLOWS
- Creators
- PAUL S MUHLY - Department of Mathematics The University of Iowa Iowa City, Iowa 52242, USAJINGBO XIA - Department of Mathematics State University of New York at Buffalo Buffalo, New York 14214, USA
- Resource Type
- Journal article
- Publication Details
- International journal of mathematics, Vol.3(4), pp.525-579
- DOI
- 10.1142/S0129167X92000254
- ISSN
- 0129-167X
- eISSN
- 1793-6519
- Language
- English
- Date published
- 08/1992
- Academic Unit
- Mathematics; Statistics and Actuarial Science
- Record Identifier
- 9984083997402771
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