Commuter of operators in a Hilbert space

Alain Boudou and Sylvie Viguier-Pla

Journal of Multivariate Analysis, 2019, vol. 170, issue C, 244-262

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.

Keywords: Commuter; Orthogonal projectors; Partial order relation; Random measures; Spectral measures; Stationary processes; Unitary operators (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X17307418
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:170:y:2019:i:c:p:244-262

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2018.06.011

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().