Permanence of weak comparison for large subalgebras

Let A be an infinite dimensional simple unital stably finite C*-algebra and B be a large subalgebra of A . In this paper, we show that B has local weak comparison if A has local weak comparison, and A has local weak comparison if M_2(B) has local weak comparison. As a consequence, we are able to prove that A has weak comparison if and only if B has weak comparison.