The almost lattice isometric copies of \(c_{0}\) in Banach lattices. (English) Zbl 1123.46010

Chen, Jinxi

Commentat. Math. Univ. Carol. 46, No. 3, 409-412 (2005).

Summary: It is shown that if a Banach lattice \(E\) contains a copy of \(c_{0}\), then it contains an almost lattice isometric copy of \(c_{0}\). The above result is a lattice version of the well-known result of R. C. James concerning the almost isometric copies of \(c_{0}\) in Banach spaces.

MSC:

46B04	Isometric theory of Banach spaces
46B25	Classical Banach spaces in the general theory
46B42	Banach lattices

Keywords:

lattice isometry; almost lattice isometry; copy of \(c_{0}\)