- Title
- An exposition of Hilbert C-modules
- Creator
- Sokopo, Bulelani Joab
- Subject
- Mathematics Algebra
- Subject
- Functions, Continuous Mathematical analysis
- Date Issued
- 2015
- Date
- 2015
- Type
- Thesis
- Type
- Masters
- Type
- MSc
- Identifier
- http://hdl.handle.net/10948/50008
- Identifier
- vital:41974
- Description
- In trying to prove that derivations of type I AW -algebras are inner, I. Kaplansky introduced and developed the basics of the concept of Hilbert C- modules. He sought to generalize the idea of a Hilbert space by replacing the field C of all complex numbers with a general (commutative and unital) C-algebra. Twenty years later, the concept was broadened and expanded to non-commutative C-algebras by W. L. Paschke and M. A. Rieffel in their papers on inner product modules over B-algebras and induced representations of C-algebras, respectively. Since then, the theory of Hilbert C-modules has grown rapidly. It was used by G. G. Kasparov as the framework for his bivariant K-theory. More recently, Hilbert C-modules have formed the technical basis for the C*-algebraic approach to quantum group theory. The aim of this dissertation is to provide as detailed an account as possible of the theory of Hilbert C-modules, as given in a book of E. C. Lance, up to and including the KSGNS construction. The KSGNS construction, named after Kasparov, Stinespring, Gelfand, Naimark and Segal, is a generalization to Hilbert C-modules of the familiar GNS construction for C-algebras. The result by Kaplansky that all derivations of a type I AW-algebra are inner is given as an application in the final chapter of the dissertation.
- Format
- vii, 139 leaves
- Format
- Publisher
- Nelson Mandela Metropolitan University
- Publisher
- Faculty of Science
- Language
- English
- Rights
- Nelson Mandela Metropolitan University
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