On Subspace-ergodic Operators

Authors

  • Mansooreh Moosapoor Department of Mathematics, Farhangian University, Tarbiat Moallem Ave, Tehran 1998963341.

DOI:

https://doi.org/10.5614/j.math.fund.sci.2020.52.3.5

Keywords:

ergodic operators, mixing operators, subspace-ergodic operators, subspace-mixing operators.

Abstract

In this paper, we define subspace-ergodic operators and give examples of these operators. We show that by any given separable infinite-dimensional Banach space, subspace-ergodic operators can be constructed. We demonstrate that an invertible operator T is subspace-ergodic if and only if T-1 is subspace-ergodic. We prove that the direct sum of two subspace-ergodic operators is subspace-ergodic and if the direct sum of two operators is subspace-ergodic, then each of them is subspace-ergodic. Also, we investigate relations between subspace-ergodic and subspace-mixing operators. For example, we show that if T is subspace-mixing and invertible, then Tn and T-n are subspace-ergodic for n∈ℕ.

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Published

2020-12-31

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Articles