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A Strict Version of the Non-commutative Urysohn Lemma

Authors:	Gert K Pedersen

Institution:	Mathematics Institute, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark

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

Keywords:	Strictly positive element hereditary $C*$-subalgebra $Q$-commuting algebras approximative units

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