Semiprojectivity of universal 𝐶*-algebras generated by algebraic elements

Shulman, Tatiana

doi:10.1090/S0002-9939-2011-11144-4

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

Proc. Amer. Math. Soc. 140 (2012), 1363-1370

DOI: https://doi.org/10.1090/S0002-9939-2011-11144-4

Published electronically: August 9, 2011

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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 $p(x)=0$, $\|x\| \le 1$, is semiprojective and residually finite-dimensional. Applications to polynomially compact operators are given.

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