Symétries isométriques. Applications à la dualité des espaces réticulés (Q5896373)

It is shown in this paper that a non-reflexive (resp. non weakly sequentially complete) Banach lattice E satisfies the following property: For every integer n, there exists an isometric copy of \(\ell^ 1_ n\) (resp. of \(\ell_ n^{\infty})\) in a dual of finite order of E. The following problem is also investigated: Let F be a Banach lattice which is isometric to a dual Banach space, does there exist a Banach lattice \(F_*\) such that F is the dual o \(F_*\) for the Banach space and for the lattice structures? It is shown that it is indeed the case when F has an unique predual, a condition which is fulfilled in many concrete situations. Several applications are given. Moreover we give a characterization, in terms of equivalent norm, of separable Banach lattices which admit a \(\sigma\)-complete Banach lattice predual.