Riesz Reasonable Cross Norms on Tensor Products of Banach Lattices

Abstract

If E and F are Banach lattices and α is any reasonable cross norm on E ⊗ F, then there exists a reasonable cross norm | α | on E ⊗ F such that E ⊗ |α | F is a Banach lattice with respect to the ordering induced by the | α | -closure of the projective cone of E ⊗ F. The norm |α| provides a link between the Fremlin tensor product and the Wittstock normed ordered tensor product of E ⊗ F. Properties of |α|, including duals and transposes are considered. Applications to Banach latticevalued sequence spaces are given.