CONDITIONAL EXPECTATIONS ON PARTIAL GENERALIZED VON NEUMANN ALGEBRA

A. A. Tijjani and B. Dangana

Department of Mathematics, Ahmadu Bello University Zaria – Nigeria

Abstract

We have constructed Partial Generalized von Neumann Algebra and Conditional expectations have been defined on it; where we considered weak and unbounded Conditional Expectations and we found out that the unbounded conditional expectation is a proper subspace of the weak Conditional Expectation. 

Keywords:   Partial Generalized von Neumann Algebra, Conditional Expectations, von Neumann Algebra, vectors, commutants, multipliers, Partial *-algebras, partial O*-algebras.