Unbounded asymptotic equivalences of operator nets with applications


ERKURŞUN ÖZCAN N., GEZER N. A.

POSITIVITY, cilt.23, ss.829-851, 2019 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 23 Konu: 4
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s11117-018-0640-z
  • Dergi Adı: POSITIVITY
  • Sayfa Sayıları: ss.829-851

Özet

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.