Results 11 to 20 of about 26,888 (119)
Different versions of the imprimitivity theorem [PDF]
Surveys in Mathematics and its Applications, 2012 In this paper we present different versions of the imprimitivity theorem hoping that this might become a support for the ones who are interested in the subject. We start with Mackey's theorem [G.W.
Tania-Luminiţa Costache
doaj
Isometric group actions on Banach spaces and representations vanishing at infinity [PDF]
, 2006 Our main result is that the simple Lie group $G=Sp(n,1)$ acts properly isometrically on $L^p(G)$ if $p>4n+2$. To prove this, we introduce property $({\BP}_0^V)$, for $V$ be a Banach space: a locally compact group $G$ has property $({\BP}_0^V)$ if every ...
A. Guichardet +27 more
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A dichotomy property for locally compact groups [PDF]
, 2018 We extend to metrizable locally compact groups Rosenthal's theorem describing those Banach spaces containing no copy of $l_1$. For that purpose, we transfer to general locally compact groups the notion of interpolation ($I_0$) set, which was defined by ...
Ferrer, Marita +2 more
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L^2-Betti numbers and Plancherel measure
, 2013 We compute $L^2$-Betti numbers of postliminal, locally compact, unimodular groups in terms of ordinary dimensions of reduced cohomology with coefficients in irreducible unitary representations and the Plancherel measure.
Petersen, Henrik Densing, Valette, Alain
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Integrability of unitary representations on reproducing kernel spaces [PDF]
, 2014 Let g be a Banach Lie algebra and \tau : g ---> g an involution. Write g=h+q for the eigenspace decomposition of g with respect to \tau and g^c := h+iq for the dual Lie algebra.
Merigon, Stephane +2 more
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Realization of compact spaces as cb-Helson sets [PDF]
, 2015 We show that, given a compact Hausdorff space $\Omega$, there is a compact group ${\mathbb G}$ and a homeomorphic embedding of $\Omega$ into ${\mathbb G}$, such that the restriction map ${\rm A}({\mathbb G})\to C(\Omega)$ is a complete quotient map of ...
Choi, Yemon
core +2 more sources
Amenable unitary representations of locally compact groups
Inventiones Mathematicae, 1990 The concept of amenability of a locally compact group (more generally, of a homogeneous space) plays an important role in various parts of mathematics, in particular in harmonic analysis and group representation theory. In the paper under review the notion of an amenable unitary representation is introduced and successfully studied.
openaire +1 more source
On the unitary representation theory of locally compact contraction groups
, 2023 The unitary representation theory of locally compact contraction groups and their semi-direct products with $\mathbb{Z}$ is studied. We put forward the problem of completely characterising such groups which are type I or CCR and this article provides a stepping stone towards a solution to this problem. In particular, we determine new examples of type I
openaire +3 more sources
Quantum groups, property (T), and weak mixing
, 2017 For second countable discrete quantum groups, and more generally second countable locally compact quantum groups with trivial scaling group, we show that property (T) is equivalent to every weakly mixing unitary representation not having almost invariant
Brannan, Michael, Kerr, David
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Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs [PDF]
, 2011 We study Gelfand pairs for locally compact quantum groups. We give an operator algebraic interpretation and show that the quantum Plancherel transformation restricts to a spherical Plancherel transformation.
Caspers, Martijn
core +4 more sources