A limit theorem for order preserving nonexpansive operators in \(L_ 1\) (Q806019)
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scientific article; zbMATH DE number 4205205
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A limit theorem for order preserving nonexpansive operators in \(L_ 1\) |
scientific article; zbMATH DE number 4205205 |
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A limit theorem for order preserving nonexpansive operators in \(L_ 1\) (English)
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1990
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The authors prove the following theorem: Let T be an order-preserving nonexpansive operator on \(L_ 1\) which decreases the \(L_{\infty}\)- norm. Then, for every \(f\in L_ p\) \((1<p<\infty)\), the sequence \([tI+(1- t)T]^ nf\) converges weakly in \(L_ p\) for any \(t\in (0,1)\).
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order-preserving nonexpansive operator
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