Some Properties of the Quasidiagonal Extension C*algebras

Abstract:

Let 0→J→A→B→0 be a quasidiagonal extension. We show the following results: ① suppose that J and B have the weakly comparison properties, then A has the weakly comparison property. ② suppose that J and B have the strictly cancellation properties, then A has the strictly cancellation property. ③ suppose that J and B have the nunperforated properties , then A has the nunperforated property.

Key words:C*algebra; quasidiagonal extension; Cuntz semigroup