In this work, we propose a definition of comonotonicity for elements of B(H)sa, i.e. bounded self-adjoint operators defined over a complex Hilbert space H. We show that this notion of comonotonicity coincides with a form of commutativity. Intuitively, comonotonicity is to commutativity as monotonicity is to bounded variation. We also define a notion of Choquet expectation for elements of B(H)sa that generalizes quantum expectations. We characterize Choquet expectations as the real-valued functionals over B(H)sa which are comonotonic additive, c-monotone, and normalized.

Commutativity, comonotonicity, and Choquet integration of self-adjoint operators

Massimo Marinacci;Simone Cerreia-Vioglio;Fabio Maccheroni;Luigi Montrucchio
2018

Abstract

In this work, we propose a definition of comonotonicity for elements of B(H)sa, i.e. bounded self-adjoint operators defined over a complex Hilbert space H. We show that this notion of comonotonicity coincides with a form of commutativity. Intuitively, comonotonicity is to commutativity as monotonicity is to bounded variation. We also define a notion of Choquet expectation for elements of B(H)sa that generalizes quantum expectations. We characterize Choquet expectations as the real-valued functionals over B(H)sa which are comonotonic additive, c-monotone, and normalized.
2018
Marinacci, Massimo; CERREIA VIOGLIO, Simone; Maccheroni, FABIO ANGELO; Montrucchio, Luigi
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11565/4011856
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