Gelfand-Raikov theorem

Gel’fand-Raikov theorem (Гельфанд-Райков) The irreducible unitary representations of a locally compact topological group GG separates 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 : G\to U(H) such that ρ(g)ρ(h)\rho(g)\neq \rho(h).

  • Gerald B. Folland, A course in abstract harmonic analysis, Studies in Advanced Mathematics. CRC Press 1995. x+276 pp. gBooks
  • И. М. Гельфанд, Д. А. Райков, Неприводимые унитарные представления локально бикомпактных групп, Матем. сб., 13(55):2-3 (1943), 301–316, pdf (I. Gelfand, D. Raikov, “Irreducible unitary representations of locally bicompact groups”, Rec. Math. N.S., 13(55):2-3 (1943), 301–316)

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