Linear dynamics induced by odometers

Bongiorno, D.; D’Aniello, E.; Darji, U.; Di Piazza, L.

doi:10.1090/proc/15354

Linear dynamics induced by odometers
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by D. Bongiorno, E. D’Aniello, U. B. Darji and L. Di Piazza PDF

Proc. Amer. Math. Soc. 150 (2022), 2823-2837 Request permission

Abstract:

Weighted shifts are an important concrete class of operators in linear dynamics. In particular, they are an essential tool in distinguishing a variety of dynamical properties. Recently, a systematic study of dynamical properties of composition operators on $L^p$ spaces has been initiated. This class of operators includes weighted shifts and also allows flexibility in construction of other concrete examples. In this article, we study one such concrete class of operators, namely composition operators induced by measures on odometers. In particular, we study measures on odometers which induce mixing and transitive linear operators on $L^p$ spaces.

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