Publications
A. Boudou and S. Viguier-Pla (2019)
Commuter of operators in a Hilbert space.
Journal of Multivariate Analysis
170 244-262.
- Classification
- 60G57, 60G10, 60B15, 60H05
- Keywords
- Commuter,
Orthogonal projectors, Partial order relation,
Random measures, Spectral measures, Stationary processes,
Unitary operators
Abstract :
Commutativity between two stationary functions is a notion that
generalizes the concept
of stationary correlation. Two stationary functions commute if and
only if their associated
spectral measures and unitary operators commute. When the operators do
not commute,
we define the concept of commuter for two operators, and then derive
it for two projectors,
for a projector and a unitary operator, and for two unitary
operators. We establish relations
between these commuters and some other tools related to proximity
between processes.
Finally, we propose a method which retrieves the commuter for two
stationary series of
finite spectrum, and we study some convergence properties.