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Vladikavkaz. Mat. Zh., 2017, Volume 19, Number 3, Pages 3–10 (Mi vmj619)  

Blum–Hanson ergodic theorem in a Banach lattices of sequences

A. N. Azizov, V. I. Chilin

National University of Uzbekistan named after M. Ulugbek, Tashkent

Abstract: It is well known that a linear contraction $T$ on a Hilbert space has the so called Blum–Hanson property, i. e., that the weak convergence of the powers $T^n$ is equivalent to the strong convergence of Ĉesaro averages $\frac1{m+1}\sum_{n=0}^m T^{k_n}$ for any strictly increasing sequence $\{k_n\}$. A similar property is true for linear contractions on $l_p$-spaces ($1\le p<\infty$), for linear contractions on $L^1$, or for positive linear contractions on $L^p$-spaces ($1< p<\infty$). We prove that this property holds for any linear contractions on a separable $p$-convex Banach lattices of sequences.

Key words: Banach solid lattice, $p$-convexity, linear contraction, ergodic theorem.

Full text: PDF file (228 kB)
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UDC: 517.98
Received: 28.10.2016

Citation: A. N. Azizov, V. I. Chilin, “Blum–Hanson ergodic theorem in a Banach lattices of sequences”, Vladikavkaz. Mat. Zh., 19:3 (2017), 3–10

Citation in format AMSBIB
\Bibitem{AziChi17}
\by A.~N.~Azizov, V.~I.~Chilin
\paper Blum--Hanson ergodic theorem in a Banach lattices of sequences
\jour Vladikavkaz. Mat. Zh.
\yr 2017
\vol 19
\issue 3
\pages 3--10
\mathnet{http://mi.mathnet.ru/vmj619}


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