Generalized limits and a mean ergodic theorem

• Autorzy: Yuan-Chuan Li , Sen-Yen Shaw
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Banach limits; $L$-limits; states; numerical radius; reflexive space; mean ergodic theorem

Kategorie tematyczne

• 47A35: Ergodic theory
• 47A12: Numerical range, numerical radius

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 121
• Numer: 3
• Strony: 207-219

Daty

wydano

1996

otrzymano

1995-02-02

poprawiono

1996-07-15

Twórcy

autor

Yuan-Chuan Li

• Department of Mathematics, Chung Yuan University, Chung-Li, Taiwan

autor

Sen-Yen Shaw

• Department of Mathematics, National Central University, Chung-Li, Taiwan,

Bibliografia

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