On Tracial Operator Representations of Quantum Decoherence Functionals

A general `quantum history theory' can be characterised by the space of histories and by the space of decoherence functionals. In this note we consider the situation where the space of histories is given by the lattice of projection operators on an infinite dimensional Hilbert space $H$. We study operator representations for decoherence functionals on this space of histories. We first give necessary and sufficient conditions for a decoherence functional being representable by a trace class operator on $H \otimes H$, an infinite dimensional analogue of the Isham-Linden-Schreckenberg representation for finite dimensions. Since this excludes many decoherence functionals of physical interest, we then identify the large and physically important class of decoherence functionals which can be represented, canonically, by bounded operators on $H \otimes H$.Comment: 14 pages, LaTeX2

Weakly compact operators and the strong* topology for a Banach space

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A Hyperfinite Factor which is not an Injective C*-Algebra

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Non-Commutative Locally Convex Measures

This is a pre-copyedited, author-produced PDF of an article accepted for publication in Quarterly Journal of Mathematics following peer review. The version of record: José Bonet and J. D. Maitland Wright Non-Commutative Locally Convex Measures Q J Math (2011) 62 (1): 21-38 first published online June 2, 2009 doi:10.1093/qmath/hap018 is available online at: http://qjmath.oxfordjournals.org/content/62/1/21We study weakly compact operators from a C*-algebra with values in a complete locally convex space. They constitute a natural non-commutative generalization of finitely additive vector measures with values in a locally convex space. Several results of Brooks, Sato and Wright are extended to this more general setting. Building on an approach due to Sato and Wright, we obtain our theorems on non-commutative finitely additive measures with values in a locally convex space, from more general results on weakly compact operators defined on Banach spaces X whose strong dual X' is weakly sequentially complete. Weakly compact operators are also characterized by a continuity property for a certain 'Right topology' as in joint work by Peralta, Villanueva, Wright and Ylinen. © 2009. Published by Oxford University Press. All rights reserved.The research of J. B. was partially supported by MEC and FEDER Project MTM2007-62643 and by GV Project Prometeo/2008/101. The support of the University of Aberdeen and the Universidad Politecnica of Valencia is gratefully acknowledged.Bonet Solves, JA.; Wright, JDM. (2011). Non-Commutative Locally Convex Measures. Quarterly Journal of Mathematics. 62(1):21-38. https://doi.org/10.1093/qmath/hap018S213862.

On Kalmbach measurability

summary:In this note we show that, for an arbitrary orthomodular lattice $L$, when $\mu$ is a faithful, finite-valued outer measure on $L$, then the Kalmbach measurable elements of $L$ form a Boolean subalgebra of the centre of $L$

Incidence and clinical characteristics of group A rotavirus infections among children admitted to hospital in Kilifi, Kenya

Background Rotavirus, predominantly of group A, is a major cause of severe diarrhoea worldwide, with the greatest burden falling on young children living in less-developed countries. Vaccines directed against this virus have shown promise in recent trials, and are undergoing effectiveness evaluation in sub-Saharan Africa. In this region limited childhood data are available on the incidence and clinical characteristics of severe group A rotavirus disease. Advocacy for vaccine intervention and interpretation of effectiveness following implementation will benefit from accurate base-line estimates of the incidence and severity of rotavirus paediatric admissions in relevant populations. The study objective was to accurately define the incidence and severity of group A rotavirus disease in a resource-poor setting necessary to make informed decisions on the need for vaccine prevention. Methods and Findings Between 2002 and 2004 we conducted prospective surveillance for group A rotavirus infection at Kilifi District Hospital in coastal Kenya. Children < 13 y of age were eligible as "cases" if admitted with diarrhoea, and "controls" if admitted without diarrhoea. We calculated the incidence of hospital admission with group A rotavirus using data from a demographic surveillance study of 220,000 people in Kilifi District. Of 15,347 childhood admissions 3,296 (22%) had diarrhoea, 2,039 were tested for group A rotavirus antigen and, of these, 588 (29%) were positive. 372 (63%) rotavirus-positive cases were infants. Of 620 controls 19 (3.1%, 95% confidence interval [CI] 1.9–4.7) were rotavirus positive. The annual incidence (per 100,000 children) of rotavirus-positive admissions was 1,431 (95% CI 1,275–1,600) in infants and 478 (437–521) in under-5-y-olds, and highest proximal to the hospital. Compared to children with rotavirus-negative diarrhoea, rotavirus-positive cases were less likely to have coexisting illnesses and more likely to have acidosis (46% versus 17%) and severe electrolyte imbalance except hyponatraemia. In-hospital case fatality was 2% among rotavirus-positive and 9% among rotavirus-negative children. Conclusions In Kilifi > 2% of children are admitted to hospital with group A rotavirus diarrhoea in the first 5 y of life. This translates into over 28,000 vaccine-preventable hospitalisations per year across Kenya, and is likely to be a considerable underestimate. Group A rotavirus diarrhoea is associated with acute life-threatening metabolic derangement in otherwise healthy children. Although mortality is low in this clinical research setting this may not be generally true in African hospitals lacking rapid and appropriate management