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The complete continuity properties for the positive projective tensor product of atomic Banach lattices |
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| Authors: | Donghai Ji Yongjin Li Qingying Bu |
| Institution: | 1. Department of Mathematics, Harbin University of Science and Technology, Harbin, 150080, China 2. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China 3. Department of Mathematics, University of Mississippi, University, MS, 38677, USA |
| Abstract: | Let E be an atomic Banach lattice and X be a separable Banach lattice. In this paper we show that ${E \hat{\otimes}_{|\pi|} X,}$ the positive projective tensor product of E and X, has the complete continuity property (respectively, the analytic complete continuity property) if and only if both E and X have the same property. We also discuss the inheritance of type I- and type II-complete continuity properties by ${E \hat{\otimes}_{|\pi|} X}$ from E and X. |
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