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A Study On Nuclear C-Algebras

Soleimani Malekan, Meisam | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 40694 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Farhadi, Hamid Reza
  7. Abstract:
  8. In this essay we study the concepts of nuclearity in C-algebras, and amenability in Banach algebras. A proof on the "every amenable C-algebra is nuclear" is studied. A Banach algebra A is called amenable if every continous derivation D : A ! E , is inner i.e. there exists anif in this denition E is a dual Banach A-module and norm continuity replace by w-continuity then we have Connes-amenability; Connes-amenability was rst considered for von Neumann algebras in [J-K-R] (and thus should perhaps be called Johnson-Kadison-Ringrose amenability). The reason why this notion of amenability is usually associated with A. Connes are his papers [Conn 1] and [Conn 2] The name "Connes-amenability" seems to be due to Ya. Helemski. "A The concept of nuclearity in C-algebras is an older concept rst introduced by M. Takesaki in 1964; A C-algebras A is called nuclear if for every C-algebra B there is only one C-norm on A B
  9. Keywords:
  10. Amenability ; Nunclearity ; Semidis Crete ; Injective ; Tensor Product ; C* Norm

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