nLab Gelfand-Raikov theorem




The Gel’fand-Raikov theorem (Гельфанд-Райков) says that the irreducible unitary representations of a locally compact topological group GG separate its points.

In other words, for any two group elements g,hGg, h\in G there exist an irreducible unitary representation ρ:GU(H)\rho \colon G \to U(H) such that ρ(g)ρ(h)\rho(g)\neq \rho(h).


The characterization of states on group algebras and what came to be known as the Gelfand-Raikov theorem:

  • И. М. Гельфанд, Д. А. Райков, Неприводимые унитарные представления локально бикомпактных групп, Матем. сб., 13(55):2–3 (1943) 301–316 [mathnet pdf]

    Israel Gelfand, Dmitri Raikov, Irreducible unitary representations of locally bicompact groups, Recueil Mathématique. N.S., 13(55) 2–3 (1943) 301–316 [mathnet:eng/sm6181]

See also

Last revised on June 13, 2024 at 16:39:59. See the history of this page for a list of all contributions to it.