The one-sided ergodic hubert transform in banach spaces

G. U.Y. Cohen; Christophe Cuny; Michael Lin

doi:10.4064/sm196-3-3

The one-sided ergodic hubert transform in banach spaces

G. U.Y. Cohen, Christophe Cuny, Michael Lin

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hubert transform lim_n, ∑_k=1ⁿ T^kx/k. We prove that weak and strong convergence are equivalent, and in a reflexive space also sup_n ||∑_k=1ⁿ T^kx/k|| < ∞ is equivalent to the convergence. We also show that - ∑_k=1^∞ T^k/k (which converges on (I - T)X) is precisely the infinitesimal generator of the semigroup (J - T)^τ /|(I - T)X.

Original language	English
Pages (from-to)	251-263
Number of pages	13
Journal	Studia Mathematica
Volume	196
Issue number	3
DOIs	https://doi.org/10.4064/sm196-3-3
State	Published - 11 Mar 2010

Keywords

Ergodic hubert transform
Measure preserving transformations
Operator power series
Semigroup of fractional powers

ASJC Scopus subject areas

General Mathematics

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10.4064/sm196-3-3

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abstract = "Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hubert transform limn, ∑k=1n Tkx/k. We prove that weak and strong convergence are equivalent, and in a reflexive space also supn ||∑k=1n Tkx/k|| < ∞ is equivalent to the convergence. We also show that - ∑k=1∞ Tk/k (which converges on (I - T)X) is precisely the infinitesimal generator of the semigroup (J - T)τ /|(I - T)X.",

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AU - Cuny, Christophe

AU - Lin, Michael

PY - 2010/3/11

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N2 - Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hubert transform limn, ∑k=1n Tkx/k. We prove that weak and strong convergence are equivalent, and in a reflexive space also supn ||∑k=1n Tkx/k|| < ∞ is equivalent to the convergence. We also show that - ∑k=1∞ Tk/k (which converges on (I - T)X) is precisely the infinitesimal generator of the semigroup (J - T)τ /|(I - T)X.

AB - Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hubert transform limn, ∑k=1n Tkx/k. We prove that weak and strong convergence are equivalent, and in a reflexive space also supn ||∑k=1n Tkx/k|| < ∞ is equivalent to the convergence. We also show that - ∑k=1∞ Tk/k (which converges on (I - T)X) is precisely the infinitesimal generator of the semigroup (J - T)τ /|(I - T)X.

KW - Ergodic hubert transform

KW - Measure preserving transformations

KW - Operator power series

KW - Semigroup of fractional powers

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DO - 10.4064/sm196-3-3

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EP - 263

JO - Studia Mathematica

JF - Studia Mathematica

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ER -

The one-sided ergodic hubert transform in banach spaces

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Keywords

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