, Volume 23, Issue 4, pp 829–851 | Cite as

Unbounded asymptotic equivalences of operator nets with applications

  • Nazife Erkurşun-Özcan
  • Niyazi Anıl GezerEmail author


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 \(\mathfrak {c}\) and \(\mathfrak {d}\) on a vector lattice, we study \(\mathfrak {d}\)-asymptotic properties of operator nets formed by \(\mathfrak {c}\)-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 \(\mathfrak {d}\)-martingale and \(\mathfrak {d}\)-Lotz–Räbiger nets.


Unbounded convergence Asymptotic equivalence Operator nets 

Mathematics Subject Classification

47A35 47B65 46B42 54A20 



We thank the referee for his/her valuable comments and suggestions.


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Authors and Affiliations

  1. 1.Department of MathematicsHacettepe UniversityAnkaraTurkey
  2. 2.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

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