Convergence of Lotz-Raebiger nets on Banach spaces

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Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye

Tezin Onay Tarihi: 2010

Öğrenci: NAZİFE ERKURŞUN

Danışman: EDUARD EMELYANOV

Özet:

The concept of LR-nets was introduced and investigated firstly by H.P. Lotz in [27] and by F. Raebiger in [30]. Therefore we call such nets Lotz-Raebiger nets, shortly LR-nets. In this thesis we treat two problems on asymptotic behavior of these operator nets. First problem is to generalize well known theorems for Ces`aro averages of a single operator to LR-nets, namely to generalize the Eberlein and Sine theorems. The second problem is related to the strong convergence of Markov LR-nets on L1-spaces. We prove that the existence of a lower-bound functions is necessary and sufficient for asymptotic stability of LR-nets of Markov operators.