BANACH LATTICE YANG MEMUAT cO - Farikhin, Farikhin (MATEMATIKA, 2007)
Let Banach lattices E and F. Lattice homomorphism T : E Â® F is called lattice embedding if there exists positive numbers m and n such thatÂ for all xÃŽE implies m.|||| Â£ ||T()|| Â£ n.||||. In others word, Banach lattice E is said to be lattice embeddable in F if there exist closed subspace F0 Ã F such that F0 and E are lattice isomorphic. As well known that dual space of E is Levi-s, i.e. Â Â Â Â supÂ / n = 1, 2,... in E* exist for every increasing bounded (in the norm) sequences Â / n = 1, 2,... in E*. If sequences space c0 is lattice embeddable in E* then sequences space lÂ¥ is lattice embeddable in E*, within E* is dual space of E. This theorem is proven by Groenewegen in [4]. For Levi-s Banach lattice E, we proof that sequences space c0 is lattice embeddable in E if only if sequences space lÂ¥ is lattice embeddable in E. Â