A Closed Range Theorem for the Frobenius-Perron Operator and Its Application to the Spectral Analysis
Document Type
Article
Publication Date
5-15-1994
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
We use the theory of functional analysis to obtain some new general results of Frobenius-Perron operators Ps:L1(X)→L1(X) and Koopman operators US:L∞(X)→L∞(X). As an application of these results, we get new necessary and sufficient conditions for PS and US to be isometric, respectively, and so in this case the spectrum of PS is completely determined.
Publication Title
Journal of Mathematical Analysis and Applications
Volume
184
Issue
1
First Page
156
Last Page
167
Recommended Citation
Ding, J.
(1994). A Closed Range Theorem for the Frobenius-Perron Operator and Its Application to the Spectral Analysis. Journal of Mathematical Analysis and Applications, 184(1), 156-167.
Available at: https://aquila.usm.edu/fac_pubs/7250