Uniformly bounded representation

In mathematics, a uniformly bounded representation T {\displaystyle T} of a locally compact group G {\displaystyle G} on a Hilbert space H {\displaystyle H} is a homomorphism into the bounded invertible operators which is continuous for the strong operator topology, and such that sup g ∈ G ‖ T g ‖ B ( H ) {\displaystyle \sup _{g\in G}\|T_{g}\|_{B(H)}} is finite. In 1947 Béla Szőkefalvi-Nagy established that any uniformly bounded representation of the integers or the real numbers is unitarizable, i.e.

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Uniformly bounded representation

In mathematics, a uniformly bounded representation T {\displaystyle T} of a locally compact group G {\displaystyle G} on a Hilbert space H {\displaystyle H} is a homomorphism into the bounded invertible operators which is continuous for the strong operator topology, and such that sup g ∈ G ‖ T g ‖ B ( H ) {\displaystyle \sup _{g\in G}\|T_{g}\|_{B(H)}} is finite. In 1947 Béla Szőkefalvi-Nagy established that any uniformly bounded representation of the integers or the real numbers is unitarizable, i.e.

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Source: Wikipedia "Uniformly bounded representation" · CC BY-SA 4.0

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