Weighted Frobenius-Perron operators and their spectra

Jabbarzadeh, Mohammad Reza ; Hajipouri, Rana

Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 113-124.

Résumé

First, some classic properties of a weighted Frobenius-Perron operator ${\mathcal{P}}_{\phi }^u$ on $L^1(\mathrm{\Sigma })$ as a predual of weighted Koopman operator $W=u{U}_{\phi }$ on $L^{\mathrm{\infty }}(\mathrm{\Sigma })$ will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of ${\mathcal{P}}_{\phi }^u$ under certain conditions.

Détail

DOI : 10.21136/MB.2016.0079-15

Classification : 11Y50, 47A10, 47B20, 47B38
Mots-clés : Frobenius-Perron operator; Fredholm operator; spectrum