On continuity of measurable group representations and homomorphisms

• Autorzy: Yulia Kuznetsova
• Języki publikacji: EN

Abstrakty

EN

Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space ℒ(H) of bounded linear operators on H with the weak operator topology. We prove that if U is a measurable map from G to ℒ(H) then it is continuous. This result was known before for separable H. We also prove that the following statement is consistent with ZFC: every measurable homomorphism from a locally compact group into any topological group is continuous.

Kategorie tematyczne

• 43A05: Measures on groups and semigroups, etc.
• 54H11: Topological groups
• 22D10: Unitary representations of locally compact groups
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 210
• Numer: 3
• Strony: 197-208

Daty

wydano

2012

Twórcy

autor

Yulia Kuznetsova

• University of Franche-Comté, 25030 Besançon Cedex, France
• University of Luxembourg 6, rue Richard, Coudenhove-Kalergi, L-1359 Luxembourg

Identyfikatory

DOI

10.4064/sm210-3-1