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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Semiprojectivity of universal $ C^*$-algebras generated by algebraic elements


Author: Tatiana Shulman
Journal: Proc. Amer. Math. Soc. 140 (2012), 1363-1370
MSC (2010): Primary 46L05, 46L35
Published electronically: August 9, 2011
MathSciNet review: 2869120
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Abstract: Let $ p$ be a polynomial in one variable whose roots all have multiplicity more than 1. It is shown that the universal $ C^*$-algebra of a relation $ p(x)=0$, $ \Vert x\Vert \le 1$, is semiprojective and residually finite-dimensional. Applications to polynomially compact operators are given.


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Tatiana Shulman
Affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitet- sparken 5, DK-2100 Copenhagen, Denmark
Email: shulman@math.ku.dk, tatiana_shulman@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11144-4
Keywords: Projective and semiprojective $C^{*}$-algebras, stable relation, lifting problem, $M$-ideal
Received by editor(s): June 13, 2009
Received by editor(s) in revised form: January 5, 2011
Published electronically: August 9, 2011
Communicated by: Marius Junge
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.