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arXiv · 1403.2114

Asymptotic behavior of operator sequences on KB-spaces

Nazife Erkursun Ozcan
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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.

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Nazife Erkursun Ozcan. 2014-03-09. Asymptotic behavior of operator sequences on KB-spaces. https://arxiv.org/abs/1403.2114

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