Complementation in the Fremlin vector lattice symmetric tensor Products-I

Abstract

For a positive integer n and a uniformly complete vector lattice E, let n;sE denote the n-fold Fremlin vector lattice symmetric tensor product of E. We
prove that if there exists a lattice homomorphism ϕ 2 E then E is lattice isomorphic to a complemented sublattice of n;sE. Moreover, if ker(ϕ) is a  projection band in E then the image of E is also a projection band in n;sE.

Key words: Fremlin tensor product, complementation, projection band.