A new approach to the similarity problem

E. Papapetros

A new approach to the similarity problem

Operator Algebras 2024-04-04 v1

Authors: E. Papapetros

Abstract

We say that a $C^*$ -algebra $\mathcal{A}$ satisfies the similarity property ((SP)) if every bounded homomorphism $u\colon \mathcal{A} \to \mathcal{B}(\mathit{H})$ , where $\mathit{H}$ is a Hilbert space, is similar to a $*$ -homomorphism. We introduce the following hypothesis (EP). (EP): Every separably acting von Neumann algebra with a cyclic vector is hyperreflexive. We prove that under (EP), all $C^*$ -algebras satisfy (SP).

Keywords

hilbert modules c*-algebras c*-algebra

Cite

@article{arxiv.2403.19668,
  title  = {A new approach to the similarity problem},
  author = {E. Papapetros},
  journal= {arXiv preprint arXiv:2403.19668},
  year   = {2024}
}

Comments

We prove that under the hypothesis (EP): Every separably acting von Neumann algebra with a cyclic vector is hyperreflexive, all C*-algebras satisfy the similarity property

A new approach to the similarity problem

Abstract

Keywords

Cite

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