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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

When almost multiplicative morphisms
are close to homomorphisms


Author: Huaxin Lin
Journal: Trans. Amer. Math. Soc. 351 (1999), 5027-5049
MSC (1991): Primary 46L05; Secondary 46L80
DOI: https://doi.org/10.1090/S0002-9947-99-02310-7
Published electronically: August 10, 1999
MathSciNet review: 1603918
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Abstract: It is shown that approximately multiplicative contractive positive morphisms from $C(X)$ (with dim $X\le 2$) into a simple $C^*$-algebra $A$ of real rank zero and of stable rank one are close to homomorphisms, provided that certain $K$-theoretical obstacles vanish. As a corollary we show that a homomorphism $h: C(X)\to A$ is approximated by homomorphisms with finite dimensional range, if $h$ gives no $K$-theoretical obstacle.


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Additional Information

Huaxin Lin
Affiliation: Department of Mathematics, East China Normal University, Shanghai 200062, China
Address at time of publication: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222
Email: hlin@darkwing.uoregon.edu

DOI: https://doi.org/10.1090/S0002-9947-99-02310-7
Received by editor(s): April 10, 1997
Published electronically: August 10, 1999
Additional Notes: Research partially supported by NSF grant DMS 9531776
Article copyright: © Copyright 1999 American Mathematical Society

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