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- Uniformly_bounded_representation abstract "In mathematics, a uniformly bounded representation of a locally compact group on a Hilbert space is a homomorphism into the bounded invertible operators which is continuous for the strong operator topology. In 1947 Béla Szőkefalvi-Nagy established that any uniformly bounded representation of the integers or the real numbers is unitarizable, i.e. conjugate by an invertible operator to a unitary representation. For the integers this gives a criterion for an invertible operator to be similar to a unitary operator: the operator norms of all the positive and negative powers must be uniformly bounded. The result on unitarizability of uniformly bounded representations was extended in 1950 by Dixmier, Day and Nakamura-Takeda to all locally compact amenable groups, following essentially the method of proof of Sz-Nagy. The result is known to fail for non-amenable groups such as SL(2,R) and the free group on two generators. Dixmier (1950) conjectured that a locally compact group is amenable if and only if every uniformly bounded representation is unitarizable.".
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- Uniformly_bounded_representation wikiPageWikiLink Amenable_group.
- Uniformly_bounded_representation wikiPageWikiLink Burnside_group.
- Uniformly_bounded_representation wikiPageWikiLink Burnsides_problem.
- Uniformly_bounded_representation wikiPageWikiLink Béla_Szőkefalvi-Nagy.
- Uniformly_bounded_representation wikiPageWikiLink Category:Functional_analysis.
- Uniformly_bounded_representation wikiPageWikiLink Category:Operator_theory.
- Uniformly_bounded_representation wikiPageWikiLink Category:Representation_theory.
- Uniformly_bounded_representation wikiPageWikiLink Cayley_graph.
- Uniformly_bounded_representation wikiPageWikiLink Complementary_series_representation.
- Uniformly_bounded_representation wikiPageWikiLink Direct_product_of_groups.
- Uniformly_bounded_representation wikiPageWikiLink Gilles_Pisier.
- Uniformly_bounded_representation wikiPageWikiLink Hilbert_space.
- Uniformly_bounded_representation wikiPageWikiLink IMRN.
- Uniformly_bounded_representation wikiPageWikiLink Induced_representation.
- Uniformly_bounded_representation wikiPageWikiLink Jacques_Dixmier.
- Uniformly_bounded_representation wikiPageWikiLink Journal_of_Functional_Analysis.
- Uniformly_bounded_representation wikiPageWikiLink Linear_group.
- Uniformly_bounded_representation wikiPageWikiLink Locally_compact_group.
- Uniformly_bounded_representation wikiPageWikiLink Matrix_group.
- Uniformly_bounded_representation wikiPageWikiLink Möbius_transformation.
- Uniformly_bounded_representation wikiPageWikiLink Operator_norm.
- Uniformly_bounded_representation wikiPageWikiLink Seifert–van_Kampen_theorem.
- Uniformly_bounded_representation wikiPageWikiLink Strong_operator_topology.
- Uniformly_bounded_representation wikiPageWikiLink Surface_group.
- Uniformly_bounded_representation wikiPageWikiLink Tits_alternative.
- Uniformly_bounded_representation wikiPageWikiLink Tohoku_Mathematical_Journal.
- Uniformly_bounded_representation wikiPageWikiLink Tôhoku_Mathematical_Journal.
- Uniformly_bounded_representation wikiPageWikiLink Unitary_representation.
- Uniformly_bounded_representation wikiPageWikiLink Von_Neumann_conjecture.
- Uniformly_bounded_representation wikiPageWikiLinkText "Dixmier Problem".
- Uniformly_bounded_representation wikiPageWikiLinkText "Uniformly bounded representation".
- Uniformly_bounded_representation wikiPageWikiLinkText "unitarizable".
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- Uniformly_bounded_representation subject Category:Functional_analysis.
- Uniformly_bounded_representation subject Category:Operator_theory.
- Uniformly_bounded_representation subject Category:Representation_theory.
- Uniformly_bounded_representation hypernym Homomorphism.
- Uniformly_bounded_representation type Field.
- Uniformly_bounded_representation type Function.
- Uniformly_bounded_representation type Physic.
- Uniformly_bounded_representation type Thing.
- Uniformly_bounded_representation comment "In mathematics, a uniformly bounded representation of a locally compact group on a Hilbert space is a homomorphism into the bounded invertible operators which is continuous for the strong operator topology. In 1947 Béla Szőkefalvi-Nagy established that any uniformly bounded representation of the integers or the real numbers is unitarizable, i.e. conjugate by an invertible operator to a unitary representation.".
- Uniformly_bounded_representation label "Uniformly bounded representation".
- Uniformly_bounded_representation sameAs m.0k0syx6.
- Uniformly_bounded_representation sameAs Q7885145.
- Uniformly_bounded_representation sameAs Q7885145.
- Uniformly_bounded_representation wasDerivedFrom Uniformly_bounded_representation?oldid=646860179.
- Uniformly_bounded_representation isPrimaryTopicOf Uniformly_bounded_representation.