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A Strict Version
of the Non-commutative Urysohn Lemma

Author: Gert K. Pedersen
Journal: Proc. Amer. Math. Soc. 125 (1997), 2657-2660
MSC (1991): Primary 46L05
MathSciNet review: 1389532
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Abstract | References | Similar Articles | Additional Information

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 $B\cap C$.

References [Enhancements On Off] (What's this?)

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Additional Information

Gert K. Pedersen
Affiliation: Mathematics Institute, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark

Keywords: Strictly positive element, hereditary $C*$-subalgebra, $Q$-commuting algebras, approximative units
Received by editor(s): November 13, 1995
Received by editor(s) in revised form: March 21, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society