A Perron FrobeniusTheory for Representations of Locally Compact Abelian Groups.
U. Groh, G. Greiner (1983)
Mathematische Annalen
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Displaying similar documents to “On the unitary representations of abelian locally compact groups”
A Perron FrobeniusTheory for Representations of Locally Compact Abelian Groups.
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We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.
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We give a new construction of semifinite factor representations of the diffeomorphism group of euclidean space. These representations are in canonical correspondence with the finite factor representations of the inductive limit unitary group. Hence, many of these representations are given in terms of quasi-free representations of the canonical commutation and anti-commutation relations. To establish this correspondence requires a generalization of complete positivity as developed in...
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In the first part of the paper, some criteria of continuity of representations of a Polish group in a Banach algebra are given. The second part uses the result of the first part to deduce automatic continuity results of Baire morphisms from Polish groups to locally compact groups or unitary groups. In the final part, the spectrum of an element in the range of a strongly but not norm continuous representation is described.
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Walter Schempp, Bernd Dreseler (1973)
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Saturation on Locally Compact Abelian Groups.
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We show that in every Polish, abelian, non-locally compact group G there exist non-Haar null sets A and B such that the set {g ∈ G; (g+A) ∩ B is non-Haar null} is empty. This answers a question posed by Christensen.