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 , of -commuting, hereditary -subalgebras of a unital -algebra , such that is -unital and , there is an element in , with , such that is strictly positive in and is strictly positive in in . Moreover, is strictly positive in in .

**[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 -algebras*, J. Funct. Anal.**6**(1970), 305-317. MR**43:934****[3]**C.A. Akemann,*A Gelfand representation theory for -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 -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 -algebras: Pushing forward the Busby invariant*, Advances in Math., to appear.**[7]**T.A. Loring,*``Lifting Solutions to Perturbing Problems in -Algebras''*, Fields Institute Monographs 8, Amer. Math. Soc., Providence, 1997.**[8]**G.K. Pedersen,*``-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