Generalization of Eberlein's and sine's ergodic theorems to lr-nets
Author: Emelyanov Eduard, Nazife Erkusan
Journal: Владикавказский математический журнал @vmj-ru
Article in issue: 3 т.9, 2007.
Free access
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. Rabiger, and was announced without a proof in [1].
Banach space, operator net, lr-net, strong convergence
Short address: https://sciup.org/14318216
IDR: 14318216
References Generalization of Eberlein's and sine's ergodic theorems to lr-nets
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