Tracial Approximations and Graph algebras on -algebra with contractive projective on Banach algebra

Abstract

We study the tracially approximation of a class of -algebra. A classification is given of certain separable unclear -algebras not necessarily of real rank zero, namely, the class of separable simple -algebras which are inductive limits of continuous-trace -algebra whose building blocks has spectrum homomorphic to the closed interval of zero and one. We introduce and study the -algebra associated with topological graphs. We show a sufficient conditions on topological graphs so that associated -algebras are simple and purely infinite. We also show the properties of projections of norm one on general Banach algebras. We give the relation of conditional expectation for algebras in harmonic analysis.