Asymptotic behavior of operator sequences on KB-spaces
Functional Analysis
2016-01-12 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1403.2114,
title = {Asymptotic behavior of operator sequences on KB-spaces},
author = {Nazife Erkursun Ozcan},
journal= {arXiv preprint arXiv:1403.2114},
year = {2016}
}
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10 Pages