Few remarks on individual ergodic theorem and summability methods (Q2732348)
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scientific article; zbMATH DE number 1623603
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Few remarks on individual ergodic theorem and summability methods |
scientific article; zbMATH DE number 1623603 |
Statements
23 July 2001
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Cesàro means
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spectral measure
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Borel summability method
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non-contractive normal operators
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spectral representation
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Few remarks on individual ergodic theorem and summability methods (English)
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The Borel summability method \(B_\alpha\) is applied to non-contractive normal operators.NEWLINENEWLINENEWLINEThe main result: Let \(x= \int_\Delta xE(dx)\) be the spectral representation of a normal operator \(x\). If NEWLINE\[NEWLINE\int_{|x|\leq 1} {\|E(dx)f\|^2\over|1-x|}< \infty,NEWLINE\]NEWLINE then \(x^kf\to\widetilde f(B_{{1\over 2}})\) a.s.NEWLINENEWLINENEWLINEThe author expresses possibilities to extend the result of the paper.
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