Operator theory and function theory in Drury-Arveson space and its quotients

The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page

Interpolation Problems For Ideals In Nest-Algebras

WOS: A1992HB13100014Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation Tx(i) = y(i), for i = 1,2,...,n. In this article, we continue the investigation of the one-vector interpolation problem for nest algebras that was begun by Lance. In particular, we require the interpolating operator to belong to certain ideals which have proved to be of importance in the study of nest algebras, namely, the compact operators, the radical, Larson's ideal, and certain other ideals. We obtain necessary and sufficient conditions for interpolation in each of these cases

Interpolation Problems For Hilbert-Schmidt Operators In Reflexive Algebras

WOS: A1993MG9860000

Cyberbullying in social networking sites and blogs : legal issues for young people and schools

This article examines the social networking phenomenon that has been so readily embraced by school-age adolescents, in the context of its potential to contribute further to the mechanisms for and incidence of cyberbullying amongst school students. Cyberbullying in these online for a, as a misuse of technology to harass, intimidate, tease, threaten, abuse or otherwise terrorise peers, teachers and/or the school in general, is discussed from both the psychological perspective and in terms of its legal ramifications (both criminal and civil) in Australia. Some recommendations for proactive and preventative measures, education and policy adoptions are provided, together with general advice to parents, schools and adolescents on awareness of the risks involved and how young people might better protect themselves in light of that knowledge

Deciphering the Acylation Pattern of Yersinia enterocolitica Lipid A

<div><p>Pathogenic bacteria may modify their surface to evade the host innate immune response. <em>Yersinia enterocolitica</em> modulates its lipopolysaccharide (LPS) lipid A structure, and the key regulatory signal is temperature. At 21°C, lipid A is hexa-acylated and may be modified with aminoarabinose or palmitate. At 37°C, <em>Y. enterocolitica</em> expresses a tetra-acylated lipid A consistent with the 3′-O-deacylation of the molecule. In this work, by combining genetic and mass spectrometric analysis, we establish that <em>Y. enterocolitica</em> encodes a lipid A deacylase, LpxR, responsible for the lipid A structure observed at 37°C. Western blot analyses indicate that LpxR exhibits latency at 21°C, deacylation of lipid A is not observed despite the expression of LpxR in the membrane. Aminoarabinose-modified lipid A is involved in the latency. 3-D modelling, docking and site-directed mutagenesis experiments showed that LpxR D31 reduces the active site cavity volume so that aminoarabinose containing Kdo₂-lipid A cannot be accommodated and, therefore, not deacylated. Our data revealed that the expression of <em>lpxR</em> is negatively controlled by RovA and PhoPQ which are necessary for the lipid A modification with aminoarabinose. Next, we investigated the role of lipid A structural plasticity conferred by LpxR on the expression/function of <em>Y. enterocolitica</em> virulence factors. We present evidence that motility and invasion of eukaryotic cells were reduced in the <em>lpxR</em> mutant grown at 21°C. Mechanistically, our data revealed that the expressions of <em>flhDC</em> and <em>rovA</em>, regulators controlling the flagellar regulon and invasin respectively, were down-regulated in the mutant. In contrast, the levels of the virulence plasmid (pYV)-encoded virulence factors Yops and YadA were not affected in the <em>lpxR</em> mutant. Finally, we establish that the low inflammatory response associated to <em>Y. enterocolitica</em> infections is the sum of the anti-inflammatory action exerted by pYV-encoded YopP and the reduced activation of the LPS receptor by a LpxR-dependent deacylated LPS.</p> </div