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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on the $L^ p$ analogue of the “zero-two” law


Author: Daniel Berend
Journal: Proc. Amer. Math. Soc. 114 (1992), 95-97
MSC: Primary 47A35; Secondary 47B38
DOI: https://doi.org/10.1090/S0002-9939-1992-1057949-4
MathSciNet review: 1057949
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Abstract: It was proved by R. Wittmann [2] that, given a positive linear contraction of ${L^p}\left ( {1 \leq p < \infty } \right ),{\operatorname {sup} _{{{\left \| f \right \|}_p} \leq 1}}{\operatorname {lim} _{n \to \infty }}\left \| {{T^n}f - {T^{n + 1}}f} \right \|$ is either $\geq {\alpha _p}{\text {or}}0$; the (best possible) value of ${\alpha _p}$ is the ${l_p}$-norm of a certain $3 \times 3$ matrix. In this paper ${\alpha _p}$ is explicitly expressed as a function of $p$.


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Keywords: "Zero-two" law, linear contraction, positive contraction
Article copyright: © Copyright 1992 American Mathematical Society