Convergence of lotz-raebiger nets on banach spaces

Erkurşun, Nazife
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.
Citation Formats
N. Erkurşun, “Convergence of lotz-raebiger nets on banach spaces,” Ph.D. - Doctoral Program, Middle East Technical University, 2010.