Proximity Between Selfadjoint Operators and Between Their Associated Random Measures

Alain Boudou, Sylvie Viguier-Pla

Abstract

We study how the proximity between two
selfadjoint bounded operators, measured by a classical distance, can
be expressed by a proximity between the associated spectral
measures. This last proximity is based on a partial order relation on the set
of projectors. Assuming an hypothesis of commutativity, we show that
the proximity between operators implies the one between the
associated spectral measures, and conversally, the proximity between
spectral measures implies the one between associated selfadjoint operators.

Keywords

Random measures, Stationary processes, Convolution, Spectral measures

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