Asymptotic behavior of operator sequences on KB-spaces


ERKURŞUN ÖZCAN N.

POSITIVITY, cilt.22, sa.3, ss.803-814, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 22 Konu: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s11117-017-0545-2
  • Dergi Adı: POSITIVITY
  • Sayfa Sayıları: ss.803-814

Özet

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.