On Banach lattices with Levi norms
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.135, sa.4, ss.1059-1063, 2007 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 135 Sayı: 4
- Basım Tarihi: 2007
- Doi Numarası: 10.1090/s0002-9939-06-08536-4
- Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1059-1063
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Gazi Üniversitesi Adresli: Evet
Özet
Schmidt proved that an operator T from a Banach lattice E into a Banach lattice G with property ( P) is order bounded if and only if its adjoint is order bounded, and in this case T satisfies vertical bar parallel to T vertical bar parallel to=vertical bar parallel to T'vertical bar parallel to. In the present paper the result is generalized to Banach lattices with Levi-Fatou norm serving as range, and some characterizations of Banach lattices with a Levi norm are given. Moreover, some characterizations of Riesz spaces having property (b) are also obtained.