The lattice-almost isometric copies of $l^{1}$ and $l^{\infty}$ in Banach lattices

Abstract: In this paper it is shown that if a Banach lattice $E$ contains a lattice copy of $l^{1}$ (or $l^{\infty}$), then it contains a lattice-almost isometric copy of $l^{1}$ (resp. $l^{\infty}$). The above result is a lattice version of the well-known results of James and Partington concerning the almost isometric copies of $l^{1}$ and $l^{\infty}$ in Banach spaces.

Keywords: Banach lattice, lattice-almost isometry, copy of $l^{1}$ (or $l^{\infty}$).

Classification (MSC2000): 46B04; 46B25, 46B42

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