On the uniform ergodic theorem in Banach spaces that do not contain duals

• Autorzy: Vladimir Fonf , Michael Lin , Alexander Rubinov
• Języki publikacji: EN

Abstrakty

EN

Let T be a power-bounded linear operator in a real Banach space X. We study the equality (*) $(I-T)X = {z ∈ X: sup_{n} ∥∑_{k=0}^{n} T^{k}z∥ < ∞}$. For X separable, we show that if T satisfies and is not uniformly ergodic, then $\overline{(I-T)X}$ contains an isomorphic copy of an infinite-dimensional dual Banach space. Consequently, if X is separable and does not contain isomorphic copies of infinite-dimensional dual Banach spaces, then (*) is equivalent to uniform ergodicity. As an application, sufficient conditions for uniform ergodicity of irreducible Markov chains on the (positive) integers are obtained.

Kategorie tematyczne

• 60J35: Transition functions, generators and resolvents
• 47A35: Ergodic theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 121
• Numer: 1
• Strony: 67-85

Daty

wydano

1996

otrzymano

1996-02-26

poprawiono

1996-04-26

Twórcy

autor

Vladimir Fonf

• Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel,

autor

Michael Lin

• Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel,

autor

Alexander Rubinov

• Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel,

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