Continuity of spectral radius and type I $C^*$-algebras

Tatiana Shulman

Continuity of spectral radius and type I $C^*$-algebras

Operator Algebras 2018-04-05 v4

Authors: Tatiana Shulman

Abstract

It is shown that the spectral radius is continuous on a $C^*$ -algebra if and only if the $C^*$ -algebra is type I. This answers a question of V. Shulman and Yu.~Turovskii [10]. It is shown also that the closure of nilpotents in a $C^*$ -algebra contains an element with non-zero spectrum if and only if the $C^*$ -algebra is not type I.

Keywords

spectral radius type I $C^*$-algebra nilpotents continuity operator algebra

Cite

@article{arxiv.1707.08848,
  title  = {Continuity of spectral radius and type I $C^*$-algebras},
  author = {Tatiana Shulman},
  journal= {arXiv preprint arXiv:1707.08848},
  year   = {2018}
}

Comments

Thanks to grant H2020-MSCA-RISE-2015-691246-Quantum Dynamics and Polish Government grant 3542/H2020/2016/2 are added

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