Compact and AM-compact orthogonally additive operators
Turkish Journal of Mathematics, cilt.50, sa.5, ss.1067-1076, 2026 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 50 Sayı: 5
- Basım Tarihi: 2026
- Doi Numarası: 10.55730/1300-0098.3782
- Dergi Adı: Turkish Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM), Academic Search Ultimate (EBSCO)
- Sayfa Sayıları: ss.1067-1076
- Anahtar Kelimeler: AM-compact orthogonally additive operator, Banach lattice, compact orthogonally additive operator, orthogonally additive operator, Riesz space
- Gazi Üniversitesi Adresli: Evet
Özet
We show that compactness of orthogonally additive operators between Banach lattices is not preserved under taking the modulus by constructing a nonlinear analogue of Krengel’s example. In contrast, for operators from a Banach lattice into an AM-space, AM-compactness is stable under lattice operations. Moreover, the space of absolutely norm-bounded, AM-compact, orthogonally additive operators from a Banach lattice into an AM-space is itself a Banach lattice. For such AM-spaces with the weak Fatou property, norm boundedness coincides with absolute norm boundedness.