Schauder decompositions and the Fremlin projective tensor product of Banach lattices |
| |
Authors: | Qingying Bu Gerard Buskes |
| |
Affiliation: | Department of Mathematics, University of Mississippi, University, MS 38677, USA |
| |
Abstract: | In this paper, we first introduce a lattice decomposition and finite-dimensional lattice decomposition (FDLD) for Banach lattices. Then we show that for a Banach lattice with FDLD, the following are equivalent: (i) it has the Radon-Nikodym property; (ii) it is a KB-space; (iii) it is a Levi space; and (iv) it is a σ-Levi space. We then give a sequential representation of the Fremlin projective tensor product of an atomic Banach lattice with a Banach lattice. Using this sequential representation, we show that if one of the Banach lattices X and Y is atomic, then the Fremlin projective tensor product has the Radon-Nikodym property (or, respectively, is a KB-space) if and only if both X and Y have the Radon-Nikodym property (or, respectively, are KB-spaces). |
| |
Keywords: | Banach lattice Projective tensor product Schauder decomposition Radon-Nikodym property |
本文献已被 ScienceDirect 等数据库收录! |
|