On Subspace-ergodic Operators
DOI:
https://doi.org/10.5614/j.math.fund.sci.2020.52.3.5Keywords:
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 onlyif 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??.
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