Nonstandard hulls of lattice-normed ordered vector spaces

Aydin A., Gorokhova S., Gul H.

TURKISH JOURNAL OF MATHEMATICS, cilt.42, sa.1, ss.155-163, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 1
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1612-59
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.155-163
  • Anahtar Kelimeler: Vector lattice, ordered vector space, lattice-normed space, decomposable lattice norm, associated Banach-Kantorovich space, lattice-normed ordered vector space, nonstandard hull
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

Nonstandard hulls of a vector lattice were introduced and studied in many papers. Recently, these notions were extended to ordered vector spaces. In the present paper, following the construction of associated Banach-Kantorovich space due to Emelyanov, we describe and investigate the nonstandard hull of a lattice-normed space, which is the foregoing generalization of Luxemburg's nonstandard hull of a normed space.