Student:	Tuncay KOR
Supervisor:	Prof. Dr. Abdugafur RAKHIMOV
Department:	Mathematics
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University, Turkey

Title of the Thesis:	Von Neumann Coupling Constant of Real W* -Algebras
Level:	M.Sc.
Acceptance Date:	30/6/2006
Number of Pages:	115
Registration Number:	i1689

Summary:

As it is known, the Theory of Operator Algebras (C* and W* - Algebras) is generally

considered over the Complex Hilbert spaces and it is studied in deep in terms of

classification. Recently, it is obtained in the literature that there is a substantial

development in the theory of operator algebras on real Hilbert spaces as the theory of

operator algebras on Complex Hilbert spaces. In this study, as a first step we studied the

concept of index which has an important role the classification of real W* -algebras.

Therefore, the canonical *-representation of finite real W* -algebras is obtained in this

study. Then, Real Von Neumann Coupling Constant concept was defined by proving the

theorem about canonical *-representation. At the end of the study, some important

properties of the coupling constant were proved and coupling constant was calculated for

real matrix algebras.

Keywords: Real factors, Von Neuman Coupling Constant.