The one-sided ergodic Hilbert transform in Banach spaces

• Autorzy: Guy Cohen , Christophe Cuny , Michael Lin
• Języki publikacji: EN

Abstrakty

EN

Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hilbert transform $lim_{n} ∑_{k=1}^{n} (T^{k}x)/k$. We prove that weak and strong convergence are equivalent, and in a reflexive space also $sup_{n} ||∑_{k=1}^{n} (T^{k}x)/k|| < ∞$ 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 $(I-T)^{r}_{|\overline{(I-T)X}}$.

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 37A05: Measure-preserving transformations
• 47A35: Ergodic theory
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 196
• Numer: 3
• Strony: 251-263

Daty

wydano

2010

Twórcy

autor

Guy Cohen

• Department of Electrical Engineering, Ben-Gurion University, Beer Sheva 84105, Israel

autor

Christophe Cuny

• Equipe ERIM, University of New Caledonia, Nouméa, New Caledonia

autor

Michael Lin

• Department of Mathematics, Ben-Gurion University, Beer Sheva 84105, Israel

Identyfikatory

DOI

10.4064/sm196-3-3