Nazife Erkursun Ozcan
Published 2014-03-09, updated 2016-01-10Version 2
The concept of an attractor or constrictor was used by several mathematicians to characterize the asymptotic behavior of operators. In this paper we show that a positive LR-net on KB-spaces is mean ergodic if the LR-net has a weakly compact attractor. Moreover if the weakly compact attractor is an order interval, then a Markovian LR-net converges strongly to the finite dimensional fixed space. As a consequence we investigate also stability of LR-nets of positive operators and existence of lower bound functions on KB-spaces.
On the convergence of products of operator nets
Asymptotic properties of $C_0$-semigroups under perturbations
Estimates for the asymptotic behavior of the constants in the Bohnenblust--Hille inequality
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