ON OPERATOR THEORETICAL ASPECTS OF LATTICE PSEUDONORMED LATTICES

Erkurşun Özcan N., Gezer N. A.

Uzbek Mathematical Journal, cilt.67, sa.3, ss.71-83, 2023 (Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 67 Sayı: 3
  • Basım Tarihi: 2023
  • Doi Numarası: 10.29229/uzmj.2023-3-9
  • Dergi Adı: Uzbek Mathematical Journal
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.71-83
  • Hacettepe Üniversitesi Adresli: Evet

Özet

A lattice pseudonormed lattice is a triplet (X, ρ, E) where X and E are vector lattices and ρ: X → E+ is an E-valued pseudonorm on X. By abstracting order theoretical properties of the norm of an AM-space with a strong norm unit to the case of lattice pseudonormed lattices, we obtain various distinct and special classes of lattice valued pseudonorms on X. By using these classes, we study properties of pseudonorm compact, pseudo-semicompact, order-AM-compact, and pseudo-AM-compact operators defined between lattice pseudonormed lattices.