Abstract
There is an important class of C*-algebras called the Type I C*-algebras, which can be characterized in several apparently different ways, which is precisely the class of C*-algebras with “tractable” representation theory and which therefore has traditionally been regarded as the class of “reasonable” C*-algebras whose structure can be “understood.” Although in recent years the structure theory of C*-algebras has been largely divorced from representation theory and there is now a much larger class of C*-algebras whose structure can be “understood” in the modern sense, Type I C*-algebras are still very important; furthermore, the structure of Type I C*-algebras can be rather precisely described, forming a model for the structure and classification of more general classes of C*-algebras.
Keywords
- Irreducible Representation
- Conditional Expectation
- Primitive Ideal
- Positive Contraction
- Continuous Trace
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 2006 Springer
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Blackadar, B. (2006). Further Structure. In: Operator Algebras. Encyclopaedia of Mathematical Sciences, vol 122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28517-2_4
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DOI: https://doi.org/10.1007/3-540-28517-2_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28486-4
Online ISBN: 978-3-540-28517-5
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