- Tytuł:
- A generalization of the uniform ergodic theorem to poles of arbitrary order
- Autorzy:
- Burlando, Laura
- Powiązania:
- https://bibliotekanauki.pl/articles/1220846.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- We obtain a generalization of the uniform ergodic theorem to the sequence $(1//n^{p}) ⅀_{k=0}^{n-1) T^k$, where T is a bounded linear operator on a Banach space and p is a positive integer. Indeed, we show that uniform convergence of the sequence above, together with an additional condition which is automatically satisfied for p = 1, is equivalent to 1 being a pole of the resolvent of T plus convergence to zero of $∥T^{n}∥//n^{p}$. Furthermore, we show that the two conditions above, together, are also equivalent to 1 being a pole of order less than or equal to p of the resolvent of T, plus a certain condition ℇ(k,p), which is less restrictive than convergence to zero of $∥T^{n}∥//n^{p}$ and generalizes the condition (called condition (ℇ-k)) introduced by K. B. Laursen and M. Mbekhta in their paper [LM2] (dealing with the case p=1).
- Źródło:
-
Studia Mathematica; 1997, 122, 1; 75-98
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł