11,842 research outputs found
The E-theoretic descent functor for groupoids
The paper establishes, for a wide class of locally compact groupoids
, the E-theoretic descent functor at the -algebra level, in a
way parallel to that established for locally compact groups by Guentner, Higson
and Trout. The second section shows that -actions on a
-algebra , where is the unit space of , can be
usefully formulated in terms of an action on the associated bundle
. The third section shows that the functor
is continuous and exact, and uses the disintegration theory of J. Renault. The
last section establishes the existence of the descent functor under a very mild
condition on , the main technical difficulty involved being that of
finding a -algebra that plays the role of C_{b}(T,B)^{cont}$ in the
group case.Comment: 21 page
The Fourier algebra for locally compact groupoids
We introduce and investigate using Hilbert modules the properties of the
Fourier algebra A(G) for a locally compact groupoid G. We establish a duality
theorem for such groupoids in terms of multiplicative module maps. This
includes as a special case the classical duality theorem for locally compact
groups proved by P. Eymard.Comment: 31 page
Two-Photon Absorption-Molecular Structure Investigation Using a Porphycene Chromophore with Potential in Photodynamic Therapy
Group amenability properties for von Neumann algebras
In his study of amenable unitary representations, M. E. B. Bekka asked if
there is an analogue for such representations of the remarkable fixed-point
property for amenable groups. In this paper, we prove such a fixed-point
theorem in the more general context of a -amenable von Neumann algebra ,
where is a locally compact group acting on . The F{\o}lner conditions of
Connes and Bekka are extended to the case where is semifinite and admits a
faithful, semifinite, normal trace which is invariant under the action of
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