Tensor product of positive operators
by
Safak Alpay
Middle East Technical University

We study the projective tensor product E₁ \otimes_\pi E₁ of Banach lattices E₁, E₂. We show that E₁ \otimes_\pi E₂ has order continuous norm and positive Schur property if the factors have the same property.

We consider tensor products of operators and show that T₁ \otimes_\pi T₂ : X₁ \otimes_\pi X₂ --> E₁ \otimes_\pi E₂ is a semicompact operator if T_i : X_i --> _i are semicompact. We also deal with absolutely summing and majorizing operators and show that T₁ \otimes_\pi T₂ is majorizing (cone absolutely summing) if the factors are.

Date received: April 11, 2000