- Tytuł:
- Generalized limits and a mean ergodic theorem
- Autorzy:
-
Li, Yuan-Chuan
Shaw, Sen-Yen - Powiązania:
- https://bibliotekanauki.pl/articles/1220908.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Banach limits
$L$-limits
states
numerical radius
reflexive space
mean ergodic theorem - Opis:
- For a given linear operator L on $ℓ^∞$ with ∥L∥ = 1 and L(1) = 1, a notion of limit, called the L-limit, is defined for bounded sequences in a normed linear space X. In the case where L is the left shift operator on $ℓ^∞$ and $X = ℓ^∞$, the definition of L-limit reduces to Lorentz's definition of σ-limit, which is described by means of Banach limits on $ℓ^∞$. We discuss some properties of L-limits, characterize reflexive spaces in terms of existence of L-limits of bounded sequences, and formulate a version of the abstract mean ergodic theorem in terms of L-limits. A theorem of Sinclair on the form of linear functionals on a unital normed algebra in terms of states is also generalized.
- Źródło:
-
Studia Mathematica; 1996, 121, 3; 207-219
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł