BANACH LATTICE YANG MEMUAT cO

Abstract

Let Banach lattices E and F. Lattice homomorphism T : E  F is called lattice embedding if there exists positive numbers m and n such that for all xE implies m.|| ||  ||T( )||  n.|| ||. In others word, Banach lattice E is said to be lattice embeddable in F if there exist closed subspace F0  F such that F0 and E are lattice isomorphic. As well known that dual space of E is Levi-, i.e. sup{ / n = 1, 2,...} in E* exist for every increasing bounded (in the norm) sequences { / n = 1, 2,...} in E*. If sequences space c0 is lattice embeddable in E* then sequences space l is lattice embeddable in E*, within E* is dual space of E. This theorem is proven by Groenewegen in [4]. For Levi- Banach lattice E, we proof that sequences space c0 is lattice embeddable in E if only if sequences space l is lattice embeddable in E.