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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
DOI: https://doi.org/10.1090/S0002-9939-97-03861-6
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?)

  • [1] C.A. Akemann, The general Stone-Weierstrass problem, J. Funct. Anal. 4 (1969), 277-294. MR 40:4772
  • [2] C.A. Akemann, Left ideal structure of $C^{*}$-algebras, J. Funct. Anal. 6 (1970), 305-317. MR 43:934
  • [3] C.A. Akemann, A Gelfand representation theory for $C^{*}$-algebras, Pacific J. Math. 39 (1971), 1-11. MR 48:6950
  • [4] C.A. Akemann and G.K. Pedersen, Facial structure in operator algebra theory, Proc. London Math. Soc. (3) 64 (1992), 418-448. MR 93c:46016
  • [5] L.G. Brown, Semicontinuity and multipliers of $C^{*}$-algebras, Canad. J. Math. 40 (1988), 865-988. MR 90a:46148
  • [6] S. Eilers, T.A. Loring and G.K. Pedersen, Morphisms of extensions of $C^{*}$-algebras: Pushing forward the Busby invariant, Advances in Math., to appear.
  • [7] T.A. Loring, ``Lifting Solutions to Perturbing Problems in $C^{*}$-Algebras'', Fields Institute Monographs 8, Amer. Math. Soc., Providence, 1997.
  • [8] G.K. Pedersen, ``$C^{*}$-Algebras and their Automorphism Groups'', LMS monographs 14, Academic Press, London, 1979. MR 81e:46037

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Additional Information

Gert K. Pedersen
Affiliation: Mathematics Institute, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark
Email: gkped@math.ku.dk

DOI: https://doi.org/10.1090/S0002-9939-97-03861-6
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

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