Asymptotic behavior of operator sequences on KB-spaces


ERKURŞUN ÖZCAN N.

POSITIVITY, vol.22, no.3, pp.803-814, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.1007/s11117-017-0545-2
  • Title of Journal : POSITIVITY
  • Page Numbers: pp.803-814

Abstract

The concept of a constrictor was used by several mathematicians to characterize the asymptotic behavior of operators. In this paper we show that a positive LR-sequence on a KB-space is mean ergodic if the LR-sequence has a weakly compact constrictor. Moreover if a weakly compact constrictor is an order interval, then a positive LR-sequence converges strongly onto the finite dimensional fixed space. As a consequence we investigate also stability of Markovian LR-sequences and the existence of lower bound functions on KB-spaces.