Generalization of Eberlein's and Sine's ergodic theorems to \(LR\)-nets

Emel'yanov E. Yu. , Erkursun N.
Владикавказский математический журнал. . Том 9. 2007 г.. Выпуск 3.

Аннотация:
The notion of \(LR\)-nets provides an appropriate setting for study of various ergodic theorems in Banach spaces. In the present paper, we prove Theorems 2.1, 3.1 which extend Eberlein's and Sine's ergodic theorems to \(LR\)-nets. Together with Theorem 1.1, these two theorems form the necessary background for further investigation of strongly convergent \(LR\)-nets. Theorem 2.1 is due to F. Räbiger, and  was announced without a proof in [1].

Ключевые слова: Banach space, operator net, \(LR\)-net, strong convergence.

Язык статьи: Английский Загрузить полный текст