nLab Alfsen-Shultz theorem

Idea

The theorem of (Alfsen-Shultz 78) says that two C*-algebras have isomorphic state spaces precisely if as Jordan algebras they are isomorphic.

This is to some extent a Jordan algebra-analog of the Gelfand-Naimark theorem.

Related theorems

Other theorems about the foundations and interpretation of quantum mechanics include:

• order-theoretic structure in quantum mechanics

  • Kochen-Specker theorem

  • Harding-Döring-Hamhalter theorem

• Fell's theorem

• Gleason's theorem

• Wigner theorem

• Bell's theorem

• Bub-Clifton theorem

• Kadison-Singer problem

References

• Erik Alfsen, Frederic Shultz, A Gelfand Neumark theorem for Jordan algebras, Advances in Math., 28 (1978), 11-56.

• Erik Alfsen, H. Hanche-Olsen, Frederic Shultz, State spaces of $C^\ast$-algebras, Acta Math., 144 (1980), 267-305.

See also

• Frederic Shultz, Dual maps of Jordan homomorphisms and ∗-homomorphisms between $C^\ast$-algebras, Pacific J. Math. Volume 93, Number 2 (1981), 435-441 (Euclid)