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BANACH LATTICE YANG MEMUAT cO


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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 xÎE implies m.|||| £ ||T()|| £ n.||||. In others word, Banach lattice E is said to be lattice embeddable in F if there exist closed subspace F0 Í F such that F0 and E are lattice isomorphic. As well known that dual space of E is Levi-s, 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-s 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.

 

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Last update: 2024-03-27 09:40:54

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