On positive tensor products of ℓpℓp-spaces

For 1⩽p1,…,pn<∞1⩽p1,…,pn<∞, we characterize the main diagonals of the positive projective tensor product ℓp1⊗ˆ|π|⋯⊗ˆ|π|ℓpn and the positive injective tensor product ℓp1⊗̌|ϵ|⋯⊗̌|ϵ|ℓpn. Then by using these two main diagonals, we characterize the reflexivity, the property of being Kantorovich–Banach spaces, and the property of being order continuous of ℓp1⊗ˆ|π|⋯⊗ˆ|π|ℓpn and ℓp1⊗̌|ϵ|⋯⊗̌|ϵ|ℓpn, as well as the space of all regular nn-linear forms on ℓp1×⋯×ℓpnℓp1×⋯×ℓpn and the space of all regular nn-homogeneous polynomials on ℓpℓp(1⩽p<∞)(1⩽p<∞).