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An Extrapolation Theorem for Contractions with Fixed Points

Published online by Cambridge University Press:  20 November 2018

Ryotaro Sato
Ryotaro Sato*
Affiliation:
Department of Mathematics, Okayama University Okayama, 700, Japan
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In [9] de la Torre proved that if is a finite measure space and T is a linear operator on a real for some fixed p, 1 < p < ∞ , such that ||T||P ≤ 1 and simultaneously ||T||∞ ≤ l, and also such that there exists with Th = h and h≠0 a.e., then the dominated ergodic theorem holds for T, i.e. for every we have

de la Torre proved his result, by showing that the operator S, defined by Sf = (sgn h) - T(f • sgn h) for is positive, and by applying Akcoglu's theorem [1] to S.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 2 , 01 June 1981 , pp. 199 - 203
Copyright
Copyright © Canadian Mathematical Society 1981

References

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