Normed tensor products of Banach lattices

On the tensor productE⊗F of a pair of order complete Banach lattices, two cross norms (called thel-andm-norm, respectively) are introduced. These cross-norms (which depend on the order of factors, and are permuted when the latter is inverted) have the property that the respective completions ofE⊗F are Banach lattices under the ordering defined by the closure of the projective cone. Moreover, they are self-dual with respect to <E ⊗F, E’> and coincide with well-known tensor norms in important special cases.