On positive tensor products of [formula omitted]-spaces

Abstract

For 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 n-linear forms on ℓp1×⋯×ℓpn and the space of all regular n-homogeneous polynomials on ℓp(1⩽p<∞).