Some properties of the space of regular operators on atomic Banach lattices

• Autores: Qingying Bu, Yongjin Li, Xiaoping Xue
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 62, Fasc. 2, 2011, págs. 131-137
• Idioma: inglés
• DOI: 10.1007/s13348-010-0007-7
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• Resumen

  • Let {{\mathcal L}^r(E,X)} denote the space of regular linear operators from a Banach lattice E to a Banach lattice X. In this paper, we show that if E is a separable atomic Banach lattice, then {{\mathcal L}^r(E,X)} is reflexive if and only if both E and X are reflexive and each positive linear operator from E to X is compact; moreover, if E is a separable atomic Banach lattice such that E and E* are order continuous, then {{\mathcal L}^r(E,X)} has the Radon–Nikodym property (respectively, is a KB-space) if and only if X has the Radon–Nikodym property (respectively, is a KB-space) and each positive linear operator from E to X is compact.