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.

Operator systems from discrete groups

We express various sets of quantum correlations studied in the theoretical physics literature in terms of different tensor products of operator systems of discrete groups. We thus recover earlier results of Tsirelson and formulate a new approach for the study of quantum correlations. To do this we formulate a general framework for the study of operator systems arising from discrete groups. We study in detail the operator system of the free group Fn on n generators, as well as the operator systems of the free products of finitely many copies of the two-element group Z2. We examine various tensor products of group operator systems, including the minimal, the maximal, and the commuting tensor products. We introduce a new tensor product in the category of operator systems and formulate necessary and sufficient conditions for its equality to the commuting tensor product in the case of group operator systems.

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.

Quantum Chromatic Numbers via Operator Systems

We define several new types of quantum chromatic numbers of a graph and characterize them in terms of operator system tensor products. We establish inequalities between these chromatic numbers and other parameters of graphs studied in the literature and exhibit a link between them and non-signalling correlation boxes.

On subspace lattices I. Closedness type properties and tensor products

We study properties of subspace lattices related to the continuity of the map Lat and the notion of reflexivity. We characterize various “closedness” properties in different ways and give the hierarchy between them. We investigate several properties related to tensor products of subspace lattices and show that the tensor product of the projection lattices of two von Neumann algebras, one of which is injective, is reflexive.

Two-Year Monitoring of Water Samples from Dam of Iskar and the Black Sea, Bulgaria, by Molecular Analysis: Focus on <i>Mycobacteriumi> spp

The coast of the Bulgarian Black Sea is a popular summer holiday destination. The Dam of Iskar is the largest artificial dam in Bulgaria, with a capacity of 675 million m3. It is the main source of tap water for the capital Sofia and for irrigating the surrounding valley. There is a close relationship between the quality of aquatic ecosystems and human health as many infections are waterborne. Rapid molecular methods for the analysis of highly pathogenic bacteria have been developed for monitoring quality. Mycobacterial species can be isolated from waste, surface, recreational, ground and tap waters and human pathogenicity of nontuberculose mycobacteria (NTM) is well recognized. The objective of our study was to perform molecular analysis for key-pathogens, with a focus on mycobacteria, in water samples collected from the Black Sea and the Dam of Iskar. In a two year period, 38 water samples were collected-24 from the Dam of Iskar and 14 from the Black Sea coastal zone. Fifty liter water samples were concentrated by ultrafiltration. Molecular analysis for 15 pathogens, including all species of genus Mycobacterium was performed. Our results showed presence of Vibrio spp. in the Black Sea. Rotavirus A was also identified in four samples from the Dam of Iskar. Toxigenic Escherichia coli was present in both locations, based on markers for stx1 and stx2 genes. No detectable amounts of Cryptosporidium were detected in either location using immunomagnetic separation and fluorescence microscopy. Furthermore, mass spectrometry analyses did not detect key cyanobacterial toxins. On the basis of the results obtained we can conclude that for the period 2012-2014 no Mycobacterium species were present in the water samples. During the study period no cases of waterborne infections were reported.