Quotients, exactness, and nuclearity in the operator system category

We continue our study of tensor products in the operator system category. We define operator system quotients and exactness in this setting and refine the notion of nuclearity by studying operator systems that preserve various pairs of tensor products. One of our main goals is to relate these refinements of nuclearity to the Kirchberg conjecture. In particular, we prove that the Kirchberg conjecture is equivalent to the statement that every operator system that is (min,er)-nuclear is also (el,c)-nuclear. We show that operator system quotients are not always equal to the corresponding operator space quotients and then study exactness of various operator system tensor products for the operator system quotient. We prove that an operator system is exact for the min tensor product if and only if it is (min,el)-nuclear. We give many characterizations of operator systems that are (min,er)-nuclear, (el,c)-nuclear, (min,el)-nuclear and (el,max)-nuclear. These characterizations involve operator system analogues of various properties from the theory of C*-algebras and operator spaces, including the WEP and LLP.

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.

The solvable Lie group N_{6, 28}: an example of an almost C_0(\mathcal{K})-C*-algebra

Motivated by the description of the C*-algebra of the affine automorphism group N6,28 of the Siegel upper half-plane of degree 2 as an algebra of operator fields defined over the unitary dual View the MathML source of the group, we introduce a family of C*-algebras, which we call almost C0(K), and we show that the C*-algebra of the group N6,28 belongs to this class.

Multidimensional operator multipliers

We introduce multidimensional Schur multipliers and characterise them, generalising well-known results by Grothendieck and Peller. We define a multidimensional version of the two-dimensional operator multipliers studied recently by Kissin and Shulman. The multidimensional operator multipliers are defined as elements of the minimal tensor product of several C *-algebras satisfying certain boundedness conditions. In the case of commutative C*-algebras, the multidimensional operator multipliersreduce to continuousmul-tidimensional Schur multipliers. We show that the multiplierswith respect to some given representations of the corresponding C*-algebrasdo not change if the representations are replaced by approximately equivalent ones. We establish a non-commutative and multidimensional version of the characterisations by Grothendieck and Peller which shows that universal operator multipliers can be obtained ascertain weak limits of elements of the algebraic tensor product of the corresponding C *-algebras.

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in~cite{jtt}. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar

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.

Characterisations of the weak expectation property

We use representations of operator systems as quotients to deduce various characterisations of the weak expectation property (WEP) for C∗ -algebras. By Kirchberg’s work on WEP, these results give new formulations of Connes’ embedding problem.

DENSE GAS IN NEARBY GALAXIES .6. A LARGE C-12/C-13 RATIO IN A NUCLEAR STARBURST ENVIRONMENT

Toward the starburst nucleus of NGC 253, C-12/C-13 line intensity ratios from six carbon bearing molecules (CO, CN, CS, HCN, HCO+, and HNC) are used to confine the possible range of carbon and oxygen isotope ratios. A detailed analysis yields C-12/C-13 approximately 40 and O-16/O-18 approximately 200. Also reported are first detections of (CS)-C-13 and of the 0(0) - 1(-1) E line of methanol (CH3OH) in an extragalactic source.

C∗-Segal algebras with order unit

We introduce the notion of a (noncommutative) C *-Segal algebra as a Banach algebra (A, {norm of matrix}{dot operator}{norm of matrix} A) which is a dense ideal in a C *-algebra (C, {norm of matrix}{dot operator}{norm of matrix} C), where {norm of matrix}{dot operator}{norm of matrix} A is strictly stronger than {norm of matrix}{dot operator}{norm of matrix} C onA. Several basic properties are investigated and, with the aid of the theory of multiplier modules, the structure of C *-Segal algebras with order unit is determined.

Degradation of 4-fluorobiphenyl by mycorrhizal fungi as determined by (19)F nuclear magnetic resonance spectroscopy and (14)C radiolabelling analysis

The pathways of biotransformation of 4-fluorobiphenyl (4FBP) by the ectomycorrhizal fungus Tylospora fibrilosa and several other mycorrhizal fungi were investigated by using (19)F nuclear magnetic resonance (NMR) spectroscopy in combination with (14)C radioisotope-detected high-performance liquid chromatography ((14)C-HPLC). Under the conditions used in this study T. fibrillosa and some other species degraded 4FBP. (14)C-HPLC profiles indicated that there were four major biotransformation products, whereas (19)F NMR showed that there were six major fluorine-containing products. We confirmed that 4-fluorobiphen-4'-ol and 4-fluorobiphen-3'-ol were two of the major products formed, but no other products were conclusively identified. There was no evidence for the expected biotransformation pathway (namely, meta cleavage of the less halogenated ring), as none of the expected products of this route were found. To the best of our knowledge, this is the first report describing intermediates formed during mycorrhizal degradation of halogenated biphenyls.

Determining adsorbate configuration on alumina surfaces with 13C nuclear magnetic resonance relaxation time analysis

Relative strengths of surface interaction for individual carbon atoms in acyclic and cyclic hydrocarbons adsorbed on alumina surfaces are determined using chemically resolved 13C nuclear magnetic resonance (NMR) T1 relaxation times. The ratio of relaxation times for the adsorbed atoms T1,ads to the bulk liquid relaxation time T1,bulk provides an indication of the mobility of the atom. Hence a low T1,ads/T1,bulk ratio indicates a stronger surface interaction. The carbon atoms associated with unsaturated bonds in the molecules are seen to exhibit a larger reduction in T1 on adsorption relative to the aliphatic carbons, consistent with adsorption occurring through the carbon-carbon multiple bonds. The relaxation data are interpreted in terms of proximity of individual carbon atoms to the alumina surface and adsorption conformations are inferred. Furthermore, variations of interaction strength and molecular configuration have been explored as a function of adsorbate coverage, temperature, surface pre-treatment, and in the presence of co-adsorbates. This relaxation time analysis is appropriate for studying the behaviour of hydrocarbons adsorbed on a wide range of catalyst support and supported-metal catalyst surfaces, and offers the potential to explore such systems under realistic operating conditions when multiple chemical components are present at the surface.

Activated protein C inhibits lipopolysaccharide-induced nuclear translocation of nuclear factor kappaB (NF-kappaB) and tumour necrosis factor alpha (TNF-alpha) production in the THP-1 monocytic cell line

Activated protein C (APC) protects against sepsis in animal models and inhibits the lipopolysacharide (LPS)-induced elaboration of proinflammatory cytokines from monocytes. The molecular mechanism responsible for this property is unknown. We assessed the effect of APC on LPS-induced tumour necrosis factor alpha (TNF-alpha) production and on the activation of the central proinflammatory transcription factor nuclear factor-kappaB (NF-kappaB) in a THP-1 cell line. Cells were preincubated with varying concentrations of APC (200 microg/ml, 100 microg/ml and 20 microg/ml) before addition of LPS (100 ng/ml and 10 microg/ml). APC inhibited LPS-induced production of TNF-alpha both in the presence and absence of fetal calf serum (FCS), although the effect was less marked with 10% FCS. APC also inhibited LPS-induced activation of NF-kappaB, with APC (200 microg/ml) abolishing the effect of LPS (100 ng/ml). The ability of APC to inhibit LPS-induced translocation of NF-kappaB is likely to be a significant event given the critical role of the latter in the host inflammatory response.

REporting and calibration of post-bomb C-14 data

The definitive paper by Stuiver and Polach (1977) established the conventions for reporting of 14C data for chronological and geophysical studies based on the radioactive decay of 14C in the sample since the year of sample death or formation. Several ways of reporting 14C activity levels relative to a standard were also established, but no specific instructions were given for reporting nuclear weapons testing (post-bomb) 14C levels in samples. Because the use of post-bomb 14C is becoming more prevalent in forensics, biology, and geosciences, a convention needs to be adopted. We advocate the use of fraction modern with a new symbol F14C to prevent confusion with the previously used Fm, which may or may not have been fractionation corrected. We also discuss the calibration of post-bomb 14C samples and the available datasets and compilations, but do not give a recommendation for a particular dataset.