An example concerning the nonlinear pointwise ergodic theorem (Q1098080)
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scientific article; zbMATH DE number 4036528
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An example concerning the nonlinear pointwise ergodic theorem |
scientific article; zbMATH DE number 4036528 |
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An example concerning the nonlinear pointwise ergodic theorem (English)
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1987
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An example is given to show that there exists a nonlinear oprator T, \(T0=0\), and nonexpansive in \(L_ p\) \((1\leq p\leq +\infty)\), such that \(T^ ng\) converges in \(L_ p\)-norm for all \(g\in L_ p\), but \[ A_ nf\triangleq n^{-1}(f+Tf+...+T^{n-1}) \] diverges on a set of positive measure.
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pointwise ergodic theorem
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invariant measure
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Markov operator
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nonlinear oprator
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