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 $L$

Shape memory polymers based on uniform aliphatic urethane networks

Aliphatic urethane polymers have been synthesized and characterized, using monomers with high molecular symmetry, in order to form amorphous networks with very uniform supermolecular structures which can be used as photo-thermally actuable shape memory polymers (SMPs). The monomers used include hexamethylene diisocyanate (HDI), trimethylhexamethylenediamine (TMHDI), N,N,N{prime},N{prime}-tetrakis(hydroxypropyl)ethylenediamine (HPED), triethanolamine (TEA), and 1,3-butanediol (BD). The new polymers were characterized by solvent extraction, NMR, XPS, UV/VIS, DSC, DMTA, and tensile testing. The resulting polymers were found to be single phase amorphous networks with very high gel fraction, excellent optical clarity, and extremely sharp single glass transitions in the range of 34 to 153 C. Thermomechanical testing of these materials confirms their excellent shape memory behavior, high recovery force, and low mechanical hysteresis (especially on multiple cycles), effectively behaving as ideal elastomers above T{sub g}. We believe these materials represent a new and potentially important class of SMPs, and should be especially useful in applications such as biomedical microdevices