Publications
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.