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Proceedings of the American Mathematical Society

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

 

 

A note on the $ L\sp 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\Vert f ... ...eratorname{lim} _{n \to \infty }}\left\Vert {{T^n}f - {T^{n + 1}}f} \right\Vert$ 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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DOI: https://doi.org/10.1090/S0002-9939-1992-1057949-4
Keywords: "Zero-two" law, linear contraction, positive contraction
Article copyright: © Copyright 1992 American Mathematical Society