A strict version of the non-commutative Urysohn Lemma

Pedersen, Gert

doi:10.1090/S0002-9939-97-03861-6

A strict version of the non-commutative Urysohn Lemma
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by Gert K. Pedersen PDF

Proc. Amer. Math. Soc. 125 (1997), 2657-2660 Request permission

Abstract:

Given a pair $B$, $C$ of $q$-commuting, hereditary $C^{*}$-subalgebras of a unital $C^{*}$-algebra $A$, such that $B\cap C$ is $\sigma$-unital and $1\in B + C$, there is an element $h$ in $A$, with $0\le h\le 1$, such that $h$ is strictly positive in $B$ and $1 - h$ is strictly positive in in $C$. Moreover, $h - h^{2}$ is strictly positive in in $B\cap C$.

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