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.

中文翻译：

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大子代数弱比较的持久性

设 A 是一个无限维简单单位稳定有限 C*-代数，B 是 A 的一个大子代数。 在本文中，我们证明如果 A 有局部弱比较，B 有局部弱比较，如果 A 有局部弱比较，如果 $ $M_{2}(B)$$ 具有局部弱比较。因此，我们能够证明 A 具有弱比较当且仅当 B 具有弱比较。