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 617Commutativity, Comonotonicity, and Choquet Integration of Self-adjoint Operators

by S. Cerreia-Vioglio, F. Maccheroni, M. Marinacci, and L. Montrucchio

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.  

Last updated December 21, 2017