Semiprojectivity of universal C*-algebras generated by algebraic elements

Abstract

Let $p$ be a polynomial in one variable whose roots either all have multiplicity more than 1 or all have multiplicity exactly 1. It is shown that the universal $C^{\ast }$-algebra of a relation $p(x)=0$, $\Vert x\Vert \le 1$ is semiprojective. In the case of all roots multiple it is shown that the universal $C^{\ast }$-algebra is also residually finite-dimensional. Applications to polynomially compact operators are given.

In old version of this paper there was an inaccuracy, namely the result was proved only for polynomials whose all roots are multiple. In new version I added a case of polynomials whose all roots have multiplicity exactly 1.

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