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    A. Boudou and S. Viguier-Pla (2018)
    Proximity between selfadjoint operators and between their associated spectral measures.
    To appear in European Journal of Pure and Applied Mathematics

    Classification
    60G57, 60G10, 60B15, 60H05
    Keywords
    Random measures, Stationary processes, Convolution, Spectral measures
    Abstract : We study how the proximity between two selfadjoint bounded operators can be expressed as a proximity between the associated spectral measures. Between two operators, we use a classical distance. For projector-valued spectral measures, we introduce the notion of $\alpha-$equivalence, which is based on a partial order relation on the set of projectors. Assuming an hypothesis of commutativity, we show that the proximity between operators is equivalent with the proximity between the associated spectral measures. We develop the particular case where the operators are compact, and give some illustrations.