Order preserving nonexpansive operators in L 1

Ulrich Krengel, Michael Lin

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We study the limit behaviour of T k f and of Cesaro averages A n f of this sequence, when T is order preserving and nonexpansive in L 1 + . If T contracts also the L-norm, the sequence T n f converges in distribution, and A n f converges weakly in L p (1<p<∞), and also in L 1 if the measure is finite. "Speed limit" operators are introduced to show that strong convergence of A n f need not hold. The concept of convergence in distribution is extended to infinite measure spaces.

Original languageEnglish
Pages (from-to)170-192
Number of pages23
JournalIsrael Journal of Mathematics
Volume58
Issue number2
DOIs
StatePublished - 1 Jun 1987

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