Asymptotic behavior of operator sequences on KB-spaces

DOI10.1007/S11117-017-0545-2arXiv1403.2114MaRDI QIDQ6249650

Publication date: 9 March 2014

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.

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Ergodic theory of linear operators (47A35) Groups and semigroups of linear operators (47D03) Positive linear operators and order-bounded operators (47B65)

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