Semiprojectivity of universal C*-algebras generated by algebraic elements

Details Semiprojectivity of universal C*-algebras generated by algebraic elements Semiprojectivity of universal C*-algebras generated by algebraic elements

2008-10-14

arxiv.org/abs/0810.2497v4

Mathematics

Functional Analysis

In old version of this paper there was an inaccuracy, namely the result was proved only for polynomials whose all roots are mu

Scientific paper

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 $C^*$-algebra of a relation $p(x)=0$, $\|x\| \le 1$ is semiprojective. In the case of all roots multiple it is shown that the universal $C^*$-algebra is also residually finite-dimensional. Applications to polynomially compact operators are given.

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