Unbounded asymptotic equivalences of operator nets with applications


ERKURŞUN ÖZCAN N., GEZER N. A.

POSITIVITY, vol.23, no.4, pp.829-851, 2019 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.1007/s11117-018-0640-z
  • Journal Name: POSITIVITY
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.829-851
  • Keywords: Unbounded convergence, Asymptotic equivalence, Operator nets, ORDER CONVERGENCE, BEHAVIOR

Abstract

Present paper deals with applications of asymptotic equivalence relations on operator nets. These relations are defined via unbounded convergences on vector lattices. Given two convergences c and delta on a vector lattice, we study delta-asymptotic properties of operator nets formed by c-continuous operators. Asymptotic equivalences are known to be useful and extremely important tools to study infinite behaviors of strongly convergent operator nets and continuous semigroups. After giving a general theory, paper focuses on delta- martingale and delta-Lotz-Rabiger nets.