A note on topologically b-order bounded sets and generalized b-weakly compact operators

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Machrafi N., ALTIN B.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.51, sa.2, ss.483-493, 2022 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.15672/hujms.961727
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.483-493
  • Anahtar Kelimeler: b-order bounded set, order weakly compact operator, b-weakly compact operator, locally convex-solid Riesz space, Frechet lattice, Banach lattice
  • Gazi Üniversitesi Adresli: Evet

Özet

We study the class of order weakly compact operators on locally solid Riesz spaces and the introduced class of generalized b-weakly compact operators on locally convex-solid Riesz spaces. We prove as a consequence that some well-known results on b-weakly compact operators on a Banach lattice extend in an improved version to generalized b-weakly compact operators on a Frechet lattice. Mathematics Subject Classification (2020). 46A40, 46B42, 47B60