Memoirs of the American Mathematical Society 1993; 92 pp; softcover Volume: 103 ISBN10: 0821825577 ISBN13: 9780821825570 List Price: US$36 Individual Members: US$21.60 Institutional Members: US$28.80 Order Code: MEMO/103/493
 The general problem addressed in this work is to characterize the possible Banach lattice structures that a separable Banach space may have. The basic questions of uniqueness of lattice structure for function spaces have been studied before, but here the approach uses random measure representations for operators in a new way to obtain more powerful conclusions. A typical result is the following: If \(X\) is a rearrangementinvariant space on \([0,1]\) not equal to \(L_2\), and if \(Y\) is an ordercontinuous Banach lattice which has a complemented subspace isomorphic as a Banach space to \(X\), then \(Y\) has a complemented sublattice which is isomorphic to \(X\) (with one of two possible lattice structures). New examples are also given of spaces with a unique lattice structure. Readership Research mathematicians specializing in Banach space theory. Table of Contents  Introduction
 Banach lattices and Köthe function spaces
 Positive operators
 The basic construction
 Lower estimates on \(P\)
 Reduction to the case of an atomic kernel
 Complemented subspaces of Banach lattices
 Strictly \(2\)concave and strictly \(2\)convex structures
 Uniqueness of lattice structure
 Isomorphic embeddings
 References
