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HILBERT MODULES OVER LOCALLY C* – ALGEBRAS
- Autor: Maria JOITA
- An aparitie: 2006
- Numar de pagini: 146
- Format: B5
- ISBN: 973-737-128-3
Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*-algebra rather than the field of complex numbers. This theory has prove to be a convenient tool in the theory of operator algebras, allowing to study C*-algebras by studying Hilbert C*-modules over them. Thus, the theory of Hilbert C*-modules is an important tool for studying Morita equivalence of C*-algebras and its application to group representation theory and crossed product C*-algebras, K-theory and KK-theory of operator algebras, completely positive maps between C*-algebras, unbounded operators and quantum groups, vector bundles, noncommutative geometry, mathematical and theoretical physics. Beside these, theory of Hilbert C*-modules is very interesting on it’s own. Locally C*-algebras are generalizations of C*-algebras. Instead of being given by a single C*-norm, the topology of a locally C*-algebra is defined by a directed family of C*-seminorms. Such many concepts as Hilbert C*-module, adjointable operator, compact operator, (induced) representation, strong Morita equivalence can be defined with obvious modifications in the framework of locally C*-algebras. Most of the basic properties of Hilbert C*-modules are still valid for Hilbert modules over locally C*-algebras, but the proofs are not always straightforward. This book is an introduction in theory of Hilbert modules over locally C*-algebras. The author did not purpose to discuss here all aspects of Hilbert modules over locally C*-algebras, but she has tried to explain the basic notions and theorems of this theory, a number important of examples and some results about representations of locally C*-algebras. A significant part of the results presented here was obtained by the author. The detailed bibliography of theory of Hilbert C*-modules can be found in Hilbert C*-Modules Homepage.
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