Extension and Restriction of Orthogonally Additive Operators

Tulu D., TURAN B.

Siberian Mathematical Journal, cilt.66, sa.1, ss.199-206, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 66 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1134/s003744662501015x
  • Dergi Adı: Siberian Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.199-206
  • Anahtar Kelimeler: 517.98, extension of an orthogonally additive operator, order continuous operator, orthogonally additive operator, Riesz space
  • Gazi Üniversitesi Adresli: Evet

Özet

We give the extension theorem for increasing order continuous orthogonallyadditive operators which is similar to Veksler’s theorem for order continuouspositive linear operators. We also show that an orthogonally additiveoperator from a Riesz space with principal projection property toa Riesz space, is order continuous if and only if for every therestriction of to the ideal generated by is order continuous.