Semiprojectivity of universal C*-algebras generated by algebraic elements

Tatiana Shulman

Semiprojectivity of universal C*-algebras generated by algebraic elements

Functional Analysis 2011-01-21 v4 Operator Algebras

Authors: Tatiana Shulman

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 $C^*$ -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.

Keywords

c*-algebras finite-dimensional algebras hilbert modules

Cite

@article{arxiv.0810.2497,
  title  = {Semiprojectivity of universal C*-algebras generated by algebraic elements},
  author = {Tatiana Shulman},
  journal= {arXiv preprint arXiv:0810.2497},
  year   = {2011}
}

Comments

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.

Semiprojectivity of universal C*-algebras generated by algebraic elements

Abstract

Keywords

Cite

Comments

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