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Convergence Of Lotz-raebiger Nets On Banach Spaces

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.

Identiferoai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/3/12612108/index.pdf
Date01 June 2010
CreatorsErkursun, Nazife
ContributorsEmel&#039, yanov, Eduard
PublisherMETU
Source SetsMiddle East Technical Univ.
LanguageEnglish
Detected LanguageEnglish
TypePh.D. Thesis
Formattext/pdf
RightsTo liberate the content for public access

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