Reflexivity and the Grothendieck propety for positive tensor products of Banach lattices

For a Banach lattice X and an Orlicz sequence space ℓ ϕ associated to an Orlicz function ϕ, let ℓ4⊗&d4; iX denote the Fremlin projective tensor product of ℓϕ and X, and let ℓ4⊗&d5; iX denote the Wittstock injective tensor product of ℓϕ and X. In this dissertation, I obtained the following results.;If ϕ and its complementary function ϕ* satisfy the Delta 2-condition, then: (i) ( ℓ4⊗&d5; iX )* is isometrically lattice isomorphic to ℓo4⊗&d4; FX* . (ii) ℓ4⊗&d4; FX is reflexive if and only if X is reflexive and each positive operator from ℓϕ to X* is compact. (iii) ℓ4⊗&d5; iX is reflexive if and only if X is reflexive and each positive operator from ℓϕ* to X is compact. (iv) ℓp⊗&d4;F X has the Grothendieck property if and only if X has the Grothendieck property and each positive linear operator from ℓ ϕ to X* is compact. (v) ℓ4⊗&d5; iX has the Grothendieck property if and only if X has the Grothendieck property and each positive linear operator from ℓϕ* to X** is compact.