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.

Hypercyclic and mixing operator semigroups

We describe a class of topological vector spaces admitting a mixing uniformly continuous operator group $\{T_t\}_{t\in\C^n}$ with holomorphic dependence on the parameter $t$. This result covers those existing in the literature. We also
describe a class of topological vector spaces admitting no supercyclic strongly continuous operator semigroups $\{T_t\}_{t\geq 0}$.

Almost all quantum states have nonclassical correlations

Quantum discord quantifies nonclassical correlations in a quantum system including those not captured by entanglement. Thus, only states with zero discord exhibit strictly classical correlations. We prove that these states are negligible in the whole Hilbert space: typically a state picked out at random has positive discord and, given a state with zero discord, a generic arbitrarily small perturbation drives it to a positive-discord state. These results hold for any Hilbert-space dimension and have direct implications for quantum computation and for the foundations of the theory of open systems. In addition, we provide a simple necessary criterion for zero quantum discord. Finally, we show that, for almost all positive-discord states, an arbitrary Markovian evolution cannot lead to a sudden, permanent vanishing of discord.

Manual mapping of drumlins in synthetic landscapes to assess operator effectiveness

Mapped topographic features are important for understanding processes that sculpt the Earth’s surface. This paper presents maps that are the primary product of an exercise that brought together 27 researchers with an interest in landform mapping wherein the efficacy and causes of variation in mapping were tested using novel synthetic DEMs containing drumlins. The variation between interpreters (e.g. mapping philosophy, experience) and across the study region (e.g. woodland prevalence) opens these factors up to assessment. A priori known answers in the synthetics increase the number and strength of conclusions that may be drawn with respect to a traditional comparative study. Initial results suggest that overall detection rates are relatively low (34–40%), but reliability of mapping is higher (72–86%). The maps form a reference dataset.

Operator Synthesis and Tensor Products

We show that Kraus' property $ S_{\sigma }$ is preserved under taking weak* closed sums with masa-bimodules of finite width and establish an intersection formula for weak* closed spans of tensor products, one of whose terms is a masa-bimodule of finite width. We initiate the study of the question of when operator synthesis is preserved under the formation of products and prove that the union of finitely many sets of the form $ \kappa \times \lambda $, where $ \kappa $ is a set of finite width while $ \lambda $ is operator synthetic, is, under a necessary restriction on the sets $ \lambda $, again operator synthetic. We show that property $ S_{\sigma }$ is preserved under spatial Morita subordinance.

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.

Local operator multipliers and positivity

We establish an unbounded version of Stinespring's Theorem and a lifting result for Stinespring representations of completely positive modular maps defined on the space of all compact operators. We apply these results to study positivity for Schur multipliers. We characterise positive local Schur multipliers, and provide a description of positive local Schur multipliers of Toeplitz type. We introduce local operator multipliers as a non-commutative analogue of local Schur multipliers, and characterise them extending both the characterisation of operator multipliers from [16] and that of local Schur multipliers from [27]. We provide a description of the positive local operator multipliers in terms of approximation by elements of canonical positive cones.

A class of almost C_0(K)-C*-algebras

We consider in this paper the family of exponential Lie groups Gn,µ, whose Lie algebra is an extension of the Heisenberg Lie algebra by the reals and whose quotient group by the centre of the Heisenberg group is an ax + b-like group. The C*-algebras of the groups Gn,µ give new examples of almost C0(K)-C*-algebras.

Almost nothing, almost anywhere: the metal shed in Ireland

This paper argues that the modern barn in Ireland is a complex social and architectural phenomena that is without, or has yet to find, a satisfactory discourse. Emerging in the middle third of the twentieth century, the modern barn – replete with corrugated iron and I-sections – continues to represent a presence in the Irish landscape whose ubiquity is as emphatic as its flexibility. It is, however, its universal properties that begin to suggest connections with wider narratives. The modernising aspects of the barn that appear in the 1920s and 30s begin to conflate with a rhetoric of architectural modernism which was simultaneously appearing across Europe. But while the relationship between high modernism’s critique of what it divined as the inspirational qualities of utilitarian buildings – Walter Gropius on grain silos, Le Corbusier on aircraft hangers etc. – has been well-documented, in Ireland this relationship perhaps contains another layer of complexity.
The barn’s consolidation as a modern type coincided with the search for a nation’s cultural identity after centuries of colonial rule. This tended to be an introspective vision that prioritised rural space over urban space, agriculture over industry, and imagined the small farm as a central tenet in the construction of a new State. This paper suggests that the twentieth-century barn – as a product of the mechanisation of agriculture promoted by the new administrations – is an iconic structure, emblematic of attempts to reconcile the contradictory forces and imagery of modernity with the mores of a traditional society. Moreover, given a cultural purview that was often ambivalent or even hostile to the ideologies and forms of modernity, the barn in Ireland is, perhaps, not so much the inspiration but the realisation of an architectural modernism in that country at its most pervasive, enduring and unself-conscious.

Urban/rural variation in the influence of widowhood on mortality risk: a cohort study of almost 300,000 couples

Death of a spouse is associated with increased mortality risk for the surviving partner (the widowhood effect). We investigated whether the effect magnitude varied between urban, rural and intermediate areas, assembling death records (2001-2009) for a prospective cohort of 296,125 married couples in Northern Ireland. The effect was greatest during the first six months of widowhood in all areas and for both sexes. Subsequently, the effect was attenuated among men in rural and intermediate areas but persisted in urban areas (HRs and 95% CIs: rural 1.09 [0.99, 1.21]; urban 1.35 [1.26, 1.44]). Among women the effect was attenuated in all areas (rural 1.06 [0.96, 1.17]; urban 1.09 [1.01, 1.17]). The impacts of spousal bereavement varied between urban and more rural areas, possibly due to variation in social support provided by the wider community. We identify men in urban areas as being in greatest need of such support and a possible target for health interventions.