nLab
Gelfand-Neumark theorem

Context

Operator algebra

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

Idea

The Gelfand–Neumark theorem (alternative spelling transliterated from the Russian: Gel’fand–Naĭmark; Гельфанд–Наймарк) says that every C*-algebra is isomorphic to a C *C^\ast-algebra of bounded linear operators on a Hilbert space.

References

  • Israel Gelfand, Mark Neumark?, On the imbedding of normed rings into the ring of operators in Hilbert space, Recueil Mathématique 12(54):2 (1943), 197–217.

  • Wikipedia, Gelfand-Naimark theorem

Last revised on November 20, 2020 at 18:03:51. See the history of this page for a list of all contributions to it.