Invariant measures from locally bounded orbits

Abstract

[EN] Motivated by recent investigations of Sophie Grivaux and & Eacute;tienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of locally bounded orbit for a continuous linear operator T : X -> X \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T:X\longrightarrow X$$\end{document} acting on a Fr & eacute;chet space X, and we use this new notion to construct (non-trivial) T-invariant probability Borel measures on ( X , B ( X ) ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(X,\mathscr {B}(X))$$\end{document} .