Linear Dynamics Induced by Odometers

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Abstract

Weighted shifts are an important concrete class of operators inlinear dynamics. In particular, they are an essential tool in distinguishing avariety dynamical properties. Recently, a systematic study of dynamical properties of composition operators on Lp spaces has been initiated. This classof operators includes weighted shifts and also allows flexibility in constructionof other concrete examples. In this article, we study one such concrete classof operators, namely composition operators induced by measures on odometers. In particular, we study measures on odometers which induce mixing andtransitive linear operators on Lp spaces
Original languageEnglish
Number of pages10
JournalProceedings of the American Mathematical Society
Publication statusPublished - 2020

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