On the continuity of the support of masa-bimodules

We anounce results on the continuity of the map sending a masa-bimodule to its support. The proofs of the results will be published elsewhere.

Stable isomorphism of dual operator spaces

We prove that two dual operator spaces $X$ and $Y$ are stably isomorphic if and only if there exist completely isometric normal representations $phi$ and $psi$ of $X$ and $Y$, respectively, and ternary rings of operators $M_1, M_2$ such that $phi (X)= [M_2^*psi (Y)M_1]^{-w^*}$ and $psi (Y)=[M_2phi (X)M_1^*].$ We prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being stably isomorphic. We apply these operator space results to prove that certain dual operator algebras are stably isomorphic if and only if they are isomorphic. We provide examples motivated by CSL algebra theory.

Tensor products of operator systems

The purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems. After giving an axiomatic definition of tensor products in this category, we examine in detail several particular examples of tensor products, including a minimal, maximal, maximal commuting, maximal injective and some asymmetric tensor products. We characterize these tensor products in terms of their universal properties and give descriptions of their positive cones. We also characterize the corresponding tensor products of operator spaces induced by a certain canonical inclusion of an operator space into an operator system. We examine notions of nuclearity for our tensor products which, on the category of C*-algebras, reduce to the classical notion. We exhibit an operator system S which is not completely order isomorphic to a C*-algebra yet has the property that for every C*-algebra A, the minimal and maximal tensor product of S and A are equal.

On the simplicial cohomology of Banach operator algebras

We investigate the simplicial cohomology of certain Banach operator algebras. The two main examples considered are the Banach algebra of all bounded operators on a Banach space and its ideal of approximable operators. Sufficient conditions will be given forcing Banach algebras of this kind to be simplicially trivial.

Remarks on common hypercyclic vectors

We treat the question of existence of common hypercyclic vectors for families of continuous linear operators. It is shown that for any continuous linear operator T on a complex Fréchet space X and a set ? ? R+ × C which is not of zero three-dimensional Lebesgue measure, the family {a T + b I : (a, b) ? ?} has no common hypercyclic vectors. This allows to answer negatively questions raised by Godefroy and Shapiro and by Aron. We also prove a sufficient condition for a family of scalar multiples of a given operator on a complex Fréchet space to have a common hypercyclic vector. It allows to show that if D = {z ? C : | z | < 1} and f ? H8 (D) is non-constant, then the family {z Mf{star operator} : b- 1 < | z | < a- 1} has a common hypercyclic vector, where Mf : H2 (D) ? H2 (D), Mf f = f f, a = inf {| f (z) | : z ? D} and b = sup {| f (z) | : | z | ? D}, providing an affirmative answer to a question by Bayart and Grivaux. Finally, extending a result of Costakis and Sambarino, we prove that the family {a Tb : a, b ? C {set minus} {0}} has a common hypercyclic vector, where Tb f (z) = f (z - b) acts on the Fréchet space H (C) of entire functions on one complex variable.

A Systems Biology Approach Identifies SART1 as a Novel Determinant of Both 5-Fluorouracil and SN38 Drug Resistance in Colorectal Cancer

Chemotherapy response rates for advanced colorectal cancer remain disappointingly low, primarily because of drug resistance, so there is an urgent need to improve current treatment strategies. To identify novel determinants of resistance to the clinically relevant drugs 5-fluorouracil (5-FU) and SN38 (the active metabolite of irinotecan), transcriptional profiling experiments were carried out on pretreatment metastatic colorectal cancer biopsies and HCT116 parental and chemotherapy-resistant cell line models using a disease-specific DNA microarray. To enrich for potential chemoresistance-determining genes, an unsupervised bioinformatics approach was used, and 50 genes were selected and then functionally assessed using custom-designed short interfering RNA(siRNA) screens. In the primary siRNA screen, silencing of 21 genes sensitized HCT116 cells to either 5-FU or SN38 treatment. Three genes (RAPGEF2, PTRF, and SART1) were selected for further analysis in a panel of 5 colorectal cancer cell lines. Silencing SART1 sensitized all 5 cell lines to 5-FU treatment and 4/5 cell lines to SN38 treatment. However, silencing of RAPGEF2 or PTRF had no significant effect on 5-FU or SN38 sensitivity in the wider cell line panel. Further functional analysis of SART1 showed that its silencing induced apoptosis that was caspase-8 dependent. Furthermore, silencing of SART1 led to a downregulation of the caspase-8 inhibitor, c-FLIP, which we have previously shown is a key determinant of drug resistance in colorectal cancer. This study shows the power of systems biology approaches for identifying novel genes that regulate drug resistance and identifies SART1 as a previously unidentified regulator of c-FLIP and drug-induced activation of caspase-8. Mol Cancer Ther; 11(1); 119-31. (C) 2011 AACR.

Ranges of bimodule projections and reflexivity

We develop a general framework for reflexivity in dual Banach
spaces, motivated by the question of when the weak* closed linear
span of two reflexive masa-bimodules is automatically reflexive. We
establish an affirmative answer to this question in a number of
cases by examining two new classes of masa-bimodules, defined in
terms of ranges of masa-bimodule projections. We give a number of
corollaries of our results concerning operator and spectral
synthesis, and show that the classes of masa-bimodules we study are
operator synthetic if and only if they are strong operator Ditkin.

Chaotic Banach algebras

We construct an infinite dimensional non-unital Banach algebra $A$ and $a\in A$ such that the sets $\{za^n:z\in\C,\ n\in\N\}$ and $\{({\bf 1}+a)^na:n\in\N\}$ are both dense in $A$, where $\bf 1$ is the unity in the unitalization $A^{\#}=A\oplus \spann\{{\bf 1}\}$ of $A$. As a byproduct, we get a hypercyclic operator $T$ on a Banach space such that $T\oplus T$ is non-cyclic and $\sigma(T)=\{1\}$.

Disjoint mixing operators

Chan and Shapiro showed that each (non-trivial) translation operator acting on the Fréchet space of entire functions endowed with the topology of locally uniform convergence supports a universal function of exponential type zero. We show the existence of d-universal functions of exponential type zero for arbitrary finite tuples of pairwise distinct translation operators. We also show that every separable infinite-dimensional Fréchet space supports an arbitrarily large finite and commuting disjoint mixing collection of operators. When this space is a Banach space, it supports an arbitrarily large finite disjoint mixing collection of C0-semigroups. We also provide an easy proof of the result of Salas that every infinite-dimensional Banach space supports arbitrarily large tuples of dual d-hypercyclic operators, and construct an example of a mixing Hilbert space operator T so that (T,T2) is not d-mixing.

The C*-algebra of ax+b-like groups

We describe the C*-algebras of " ax+b" -like groups in terms of algebras of operator fields defined over their dual spaces.

FLT1 Genetic Variation Predisposes to Neovascular AMD in Ethnically Diverse Populations and Alters Systemic FLT1 Expression

Purpose: Current understanding of the genetic risk factors for age-related macular degeneration (AMD) is not sufficiently predictive of the clinical course. The VEGF pathway is a key therapeutic target for treatment of neovascular AMD; however, risk attributable to genetic variation within pathway genes is unclear. We sought to identify single nucleotide polymorphisms (SNPs) associated with AMD within the VEGF pathway.
Methods: Using a tagSNP, direct sequencing and meta-analysis approach within four ethnically diverse cohorts, we identified genetic risk present in FLT1, though not within other VEGF pathway genes KDR, VEGFA, or VASH1. We used ChIP and ELISA in functional analysis.
Results: The FLT1 SNPs rs9943922, rs9508034, rs2281827, rs7324510, and rs9513115 were significantly associated with increased risk of neovascular AMD. Each association was more significant after meta-analysis than in any one of the four cohorts. All associations were novel, within noncoding regions of FLT1 that do not tag for coding variants in linkage disequilibrium. Analysis of soluble FLT1 demonstrated higher expression in unaffected individuals homozygous for the FLT1 risk alleles rs9943922 (P = 0.0086) and rs7324510 (P = 0.0057). In silico analysis suggests that these variants change predicted splice sites and RNA secondary structure, and have been identified in other neovascular pathologies. These data were supported further by murine chromatin immunoprecipitation demonstrating that FLT1 is a target of Nr2e3, a nuclear receptor gene implicated in regulating an AMD pathway.
Conclusions: Although exact variant functions are not known, these data demonstrate relevancy across ethnically diverse genetic backgrounds within our study and, therefore, hold potential for global efficacy.

A function-based treatment package aiming at decreasing self-injurious behaviour and tantrums.

Self-injurious and aggressive behaviours have often been identified as the cause for students’ lack of academic progress, parental distress, health risks and teachers´ low satisfaction levels. Functional analysis has been identified in the research literature as the benchmark of effective treatments for disruptive and/or inappropriate behaviours. The present study was completed with a girl diagnosed with ASD. An experimental functional analysis was conducted identifying the function of self-injurious behaviours and tantrums to be escaping from tasks. A treatment package was consequently put in place integrating several components that aimed at reducing overall levels of inappropriate behaviours. Results showed a clear and meaningful improvement in the student´s overall health and academic progress, as well as in parental involvement, teachers’ satisfaction and school inclusion. These outcomes are discussed in the light of evidence-based experimental procedures based on applied behaviour analysis and more specifically on the functional-analytic literature, which, if put in place consistently, can bring valuable positive changes in the quality of life of individuals with ASD.

Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).

Ideals of A(G) and bimodules over maximal abelian selfadjoint algebras

This paper is concerned with weak⁎ closed masa-bimodules generated by A(G)-invariant subspaces of VN(G). An annihilator formula is established, which is used to characterise the weak⁎ closed subspaces of B(L2(G)) which are invariant under both Schur multipliers and a canonical action of M(G) on B(L2(G)) via completely bounded maps. We study the special cases of extremal ideals with a given null set and, for a large class of groups, we establish a link between relative spectral synthesis and relative operator synthesis.