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DOI: 10.23671/VNC.2017.3.7107

Blum-Hanson Ergodic Theorem in a Banach Lattices of Sequences

Azizov A. N. , Chilin V. I.
Vladikavkaz Mathematical Journal 2017. Vol. 19. Issue 3.
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 Cesaro 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.
Keywords: Banach solid lattice, \(p\)-convexity, linear contraction, ergodic theorem
Language: Russian Download the full text  
For citation: Azizov A. N., Chilin V. I. Blum-Hanson ergodic theorem in a Banach lattices of sequences // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp. 3-10. DOI 10.23671/VNC.2017.3.7107
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