Pointwise limit theorem for a class of unbounded operators in $𝕃^{r}$-spaces

• Autorzy: Ryszard Jajte
• Języki publikacji: EN

Abstrakty

EN

We distinguish a class of unbounded operators in $𝕃^{r}$, r ≥ 1, related to the self-adjoint operators in 𝕃². For these operators we prove a kind of individual ergodic theorem, replacing the classical Cesàro averages by Borel summability. The result is equivalent to a version of Gaposhkin's criterion for the a.e. convergence of operators. In the proof, the theory of martingales and interpolation in $𝕃^{r}$-spaces are applied.

Kategorie tematyczne

• 40G10: Abel, Borel and power series methods
• 47A35: Ergodic theory
• 60F15: Strong theorems
• 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 179
• Numer: 1
• Strony: 49-61

Daty

wydano

2007

Twórcy

autor

Ryszard Jajte

• Faculty of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Identyfikatory

DOI

10.4064/sm179-1-5