(untitled) (European Journal of Pure and Applied Mathematics, 2018)
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.