| Softcover ISBN: | 978-1-4704-3545-5 |
| Product Code: | MEMO/258/1240 |
| List Price: | $81.00 |
| MAA Member Price: | $72.90 |
| AMS Member Price: | $48.60 |
| Electronic ISBN: | 978-1-4704-5071-7 |
| Product Code: | MEMO/258/1240.E |
| List Price: | $81.00 |
| MAA Member Price: | $72.90 |
| AMS Member Price: | $48.60 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 258; 2019; 85 ppMSC: Primary 47; Secondary 46;
The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C\(^*\)-algebras. They make contributions to the study of C\(^*\)-envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.
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Table of Contents
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Chapters
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1. Introduction
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2. Preliminaries
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3. Definitions and Fundamental Results
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4. Maximal C$^*$-covers, Iterated Crossed Products and Takai Duality
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5. Crossed Products and the Dirichlet Property
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6. Crossed Products and Semisimplicity
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7. The Crossed Product as the Tensor Algebra of a C$^*$-correspondence.
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8. Concluding Remarks and Open Problems
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Additional Material
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The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C\(^*\)-algebras. They make contributions to the study of C\(^*\)-envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.
-
Chapters
-
1. Introduction
-
2. Preliminaries
-
3. Definitions and Fundamental Results
-
4. Maximal C$^*$-covers, Iterated Crossed Products and Takai Duality
-
5. Crossed Products and the Dirichlet Property
-
6. Crossed Products and Semisimplicity
-
7. The Crossed Product as the Tensor Algebra of a C$^*$-correspondence.
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8. Concluding Remarks and Open Problems
