Domination properties of lattice homomorphisms |
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| Authors: | Zili Chen |
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| Affiliation: | (1) Department of Mathematics, Southwest Jiaotong University, Chengdu, 610031, Peoples Republic of China |
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| Abstract: | Let E and F be Banach lattices, T, K : E → F be such that 0 ≤ T ≤ K and T is either a lattice homomorphism or almost interval-preserving. In this paper we will deduce that (1) If K is AM-compact then T also is AM-compact; (2) If either E′ or F has an order continuous norm and K is compact, then T is compact as well; (3) If K is weakly compact then so is T. Some related results are also obtained. |
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| Keywords: | Banach lattice order continuous norm lattice homomorphism compact operator weakly compact operator |
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