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We study weak limits of the extreme points, ∂ e ( E * 1), of the dual ball of a JB*-triple, E. We show that all such weak limits, except possibly the zero functional, are weak sequential limits and we discuss implications for the structure of E. [ABSTRACT FROM AUTHOR]

Discusses the socioeconomic framework of the coral reef management system applied at the Montego Bay marine park.

The main result is a representation theorem which shows that, for a large class of quantum logics, a quantum logic, Q, is isomorphic to the lattice of projective faces in a suitable convex set K. As an application we extend our earlier results [4], which, subject to countability conditions, gave a geometric characterization of those quantum logics which are isomorphic to the projection lattice of a von Neumann algebra or a J B W-algebra. [ABSTRACT FROM AUTHOR]

A problem of Mackey for von Neumann algebras has been settled by the conjunction of the early work of Gleason and the recent advances of Christensen and Yeadon. We show that Mackey's conjecture holds in much greater generality. Let A be a JBW-algebra and let L be the lattice of all projections in A. A quantum measure on L is a countably additive map, m, from L into the real numbers. Our results imply that m always has a unique extension to a bounded linear functional on A, provided that A has no Type I direct summand. [ABSTRACT FROM AUTHOR]

The problem of characterising those quantum logics which can be identified with the lattice of projections in a JBW-algebra or a von Neumann algebra is considered. For quantum logics which satisfy the countable chain condition and which have no Type I part, a characterisation in terms of geometric properties of the quantum state space is given. [ABSTRACT FROM AUTHOR]