The one-sided ergodic hubert transform in banach spaces

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

Research output: Contribution to journalArticlepeer-review

9 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 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.

Original languageEnglish
Pages (from-to)251-263
Number of pages13
JournalStudia Mathematica
Volume196
Issue number3
DOIs
StatePublished - 11 Mar 2010

Keywords

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

ASJC Scopus subject areas

  • Mathematics (all)

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