We deal with not necessarily additive functions acting on complete orthomodular posets and taking values in Hausdorff uniform spaces, where no algebraic structure is required. As a consequence, neither pseudo-additivity, nor monotonicity are meaningful notions in this setting. Conditions ensuring their boundedness are exhibited, in terms of some mild continuity properties. Such conditions are satisfied, in particular, by completely additive measures on projection lattices of von Neumann algebras. Hence, among other things, our main result provides a version in the generalized non-additive quantum setting of the so called boundedness principle in classical and quantum measure theory.

Boundedness of non-additive quantum measures

CAVALIERE, Paola;
2014

Abstract

We deal with not necessarily additive functions acting on complete orthomodular posets and taking values in Hausdorff uniform spaces, where no algebraic structure is required. As a consequence, neither pseudo-additivity, nor monotonicity are meaningful notions in this setting. Conditions ensuring their boundedness are exhibited, in terms of some mild continuity properties. Such conditions are satisfied, in particular, by completely additive measures on projection lattices of von Neumann algebras. Hence, among other things, our main result provides a version in the generalized non-additive quantum setting of the so called boundedness principle in classical and quantum measure theory.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4483857
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