The E-theoretic descent functor for groupoids

The paper establishes, for a wide class of locally compact groupoids $\Gamma$, the E-theoretic descent functor at the $C^{*}$-algebra level, in a way parallel to that established for locally compact groups by Guentner, Higson and Trout. The second section shows that $\Gamma$-actions on a $C_{0}(X)$-algebra $B$, where $X$ is the unit space of $\Gamma$, can be usefully formulated in terms of an action on the associated bundle $B^{\sharp}$. The third section shows that the functor $B\to C^{*}(\Gamma,B)$ 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 $\Gamma$, the main technical difficulty involved being that of finding a $\Gamma$-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

The regions of the herpes simplex virus type 1 immediate early protein Vmwl75 required for site specific DNA binding closely correspond to those involved in transcriptional regulation

The immediate-early (IE) protein Vmw175 (ICP4) of HSV-1 is required for the transcription of later classes of viral genes and the repression of IE gene expression. We have previously constructed a panel of plasmid-borne insertion and deletion mutants of the gene encoding Vmw175 and assayed their ability to regulate transcription in transient transfection assays. By this approach we have mapped the regions of the Vmw175 amino acid sequence that are required for transcriptional activation and repression of herpes virus promoters. This paper describes the use of nuclear extracts, made from cells transfected with these mutant plasmids, in gel retardation DNA binding assays in order to define the regions of Vmw175 involved in binding to a specific Vmw175 DNA binding site. The results show that amino acid residues 275–495 (a region which is highly conserved between Vmw175 and the varicella-zoster virus “IE” 140K protein) include structures which are critically required for specific DNA binding, transactivation and repression. This raises the interesting paradox that although the specific DNA sequence recognized by Vmw175 is not commonly found in its target promoters, the protein domain required for recognition of this sequence is required for promoter activation

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 $G$-amenable von Neumann algebra $M$, where $G$ is a locally compact group acting on $M$. The F{\o}lner conditions of Connes and Bekka are extended to the case where $M$ is semifinite and admits a faithful, semifinite, normal trace which is invariant under the action of $G$