English

On $\mathfrak{L}_{\infty}$-liftings of the Gelfand-Naimark morphism

Functional Analysis 2024-06-17 v1 Operator Algebras

Abstract

Let MM be a WW^{\ast}-algebra acting on a separable complex Hilbert space HH. We show that the inclusion of MM into B(H)\mathscr{B}(H) factors through an L\mathfrak{L}_{\infty}-space only if MM is a finite type I\mathrm{I} algebra.

Keywords

Cite

@article{arxiv.2403.01574,
  title  = {On $\mathfrak{L}_{\infty}$-liftings of the Gelfand-Naimark morphism},
  author = {Vasily Melnikov},
  journal= {arXiv preprint arXiv:2403.01574},
  year   = {2024}
}