Analogues of the “zero-two” law for positive linear contractions inL
p andC(X) |
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Authors: | Rainer Wittmann |
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Institution: | 1. Mathematisch-Geographische Fakult?t, Katholische Universit?t Eichst?tt, Ostenstra?e 26-28, D-8078, Eichst?tt, FRG
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Abstract: | LetT be a positive linear contraction inL
p (1≦p<∞), then we show that lim ‖T
pf −T
n+1
f‖
p
≦(1 − ε)21/p
(f∈L
p
+
, ε>0 independent off) implies already limn
n→∞ ‖T
nf −T
n+1
n+1f ‖p
p=0. Several other related results as well as uniform variants of these are also given. Finally some similar results inLsu/t8 andC(X) are shown. |
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Keywords: | |
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