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;
2014-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
