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.

Chronic treatment with a stable obestatin analogue significantly alters plasma triglyceride levels but fails to influence food intake, fluid intake, body weight, or body composition in rats.

Obestatin (OB(1-23) is a 23 amino acid peptide encoded on the preproghrelin gene, originally reported to have metabolic actions related to food intake, gastric emptying and body weight. The biological instability of OB(1-23) has recently been highlighted by studies demonstrating its rapid enzymatic cleavage in a number of biological matrices. We assessed the stability of both OB(1-23) and an N-terminally PEGylated analogue (PEG-OB(1-23)) before conducting chronic in vivo studies. Peptides were incubated in rat liver homogenate and degradation monitored by LC-MS. PEG-OB(1-23) was approximately 3-times more stable than OB(1-23). Following a 14 day infusion of Sprague Dawley rats with 50 mol/kg/day of OB(1-23) or a N-terminally PEGylated analogue (PEG-OB(1-23)), we found no changes in food/fluid intake, body weight and plasma glucose or cholesterol between groups. Furthermore, morphometric liver, muscle and white adipose tissue (WAT) weights and tissue triglyceride concentrations remained unaltered between groups. However, with stabilised PEG-OB(1-23) we observed a 40% reduction in plasma triglycerides. These findings indicate that PEG-OB(1-23) is an OB(1-23) analogue with significantly enhanced stability and suggest that obestatin could play a role in modulating physiological lipid metabolism, although it does not appear to be involved in regulation of food/fluid intake, body weight or fat deposition.

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.

A hypercyclic finite rank perturbation of a unitary operator

A unitary operator V and a rank 2 operator R acting on a Hilbert space H are constructed such that V + R is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.

Operators, commuting with the Volterra operator, are not weakly supercyclic

We prove that any bounded linear operator on $L_p[0,1]$ for $1\leq p

Impact of operator experience on information feedback and reusability

Keeping a record of operator experience remains a challenge to operation management and a major source of inefficiency in information management. The objective is to develop a framework that enables an explicit presentation of experience based on information use. A purposive sampling method is used to select four small and medium-sized enterprises as case studies. The unit of analysis is the production process in the machine shop. Data collection is by structured interview, observation and documentation. A comparative case analysis is applied. The findings suggest experience is an accumulation of tacit information feedback, which can be made explicit in information use interoperatability matrix. The matrix is conditioned upon information use typology, which is strategic in waste reduction. The limitations include difficulty of participant anonymity where the organisation nominates a participant. Areas for further research include application of the concepts to knowledge management and shop floor resource management.

Measuring workforce segregation: religious composition of private-sector employees at individual sites in Northern Ireland

In this paper I examine the scope of publicly available information on the religious composition of employees in private-sector companies in Northern Ireland. I highlight the unavailability of certain types of monitoring data and the impact of data aggregation at company as opposed to site level. Both oversights lead to underestimates of the extent of workplace segregation in Northern Ireland. The ability to provide more-coherent data on workplace segregation, by religion, in Northern Ireland is crucial in terms of advancing equality and other social-justice agendas. I argue that a more-accurate monitoring of religious composition of workplaces is part of an overall need to develop a spatial approach in which the importance of ethnically territorialised spaces in the reproduction of ethnosectarian disputation is understood.

Effect of composition, solvent exchange liquid and drying method on the porous structure of phenol-formaldehyde gels

Organic gels have been synthesized by sol–gel polycondensation of phenol (P) and formaldehyde (F) catalyzed by sodium carbonate (C). The effect of synthesis parameters such as phenol/catalyst ratio (P/C), solvent exchange liquid and drying method, on the porous structure of the gels have been investigated. The total and mesopore volumes of the PF gels increased with increasing P/C ratio in the range of P/C B 8, after this both properties started to decrease with P/C ratio for P/C[8 and the gel with P/C = 8 showed the highest total and mesopore volumes of 1.281 and 1.279 cm3 g-1 respectively. The gels prepared by freeze drying possessed significantly higher porosities than the vacuum dried gels. The pore volume and average pore diameter of the freeze dried gels were significantly higher than those of the vacuum dried gels. T-butanol emerged as the preferred solvent for the removal of water from the PF hydrogel prior to drying, as significantly higher pore volumes and specific surface areas were obtained in the corresponding dried gels. The results showed that freeze drying with t-butanol and lower P/C ratios were favourable conditions for the synthesis of highly mesoporous phenol–formaldehyde gels.

Composition profiling of seized ecstasy tablets by Raman spectroscopy

Raman spectroscopy with far-red excitation has been investigated as a simple and rapid technique for composition profiling of seized ecstasy (MDMA, N-methyl-3,4-methylenedioxyamphetamine) tablets. The spectra obtained are rich in vibrational bands and allow the active drug and excipient used to bulk the tablets to be identified. Relative band heights can be used to determine drug/excipient ratios and the degree of hydration of the drug while the fact that 50 tablets per hour can be analysed allows large numbers of spectra to be recorded. The ability of Raman spectroscopy to distinguish between ecstasy tablets on the basis of their chemical composition is illustrated here by a sample set of 400 tablets taken from a large seizure of > 50000 tablets that were found in eight large bags. The tablets are all similar in appearance and carry the same logo. Conventional analysis by GC-MS showed they contained MDMA. Initial Raman studies of samples from each of the eight bags showed that despite some tablet-to-tablet variation within each bag the contents could be classified on the basis of the excipients used. The tablets in five of the bags were sorbitol-based, two were cellulose-based and one bag contained tablets with a glucose excipient. More extensive analysis of 50 tablets from each of a representative series of sample bags gave distribution profiles that showed the contents of each bag were approximately normally distributed about a mean value, rather than being mixtures of several discrete types. Two of the sorbitol-containing sample sets were indistinguishable while a third was similar but not identical to these, in that it contained the same excipient and MDMA with the same degree of hydration but had a slightly different MDMA/sorbitol ratio. The cellulose-based samples were badly manufactured and showed considerable tablet-to-tablet variation in their drug/excipient ratio while the glucose-based tablets had a tight distribution in their drug/excipient ratios. The degree of hydration in the MDMA feedstocks used to manufacture the cellulose-, glucose- and sorbitol-based tablets were all different from each other. This study, because it centres on a single seizure of physically similar tablets with the same active drug, highlights the fact that simple physical descriptions coupled with active drug content do not in themselves fully characterize the nature of the seized materials. There is considerable variation in the composition of the tablets within this single seizure and the fact that this variation can be detected from Raman spectra demonstrates that the potential benefits of obtaining highly detailed spectra can indeed translate into information that is not readily available from other methods but would be useful for tracing of drug distribution networks.