Projective and injective tensor products of Banach $$L^0$$-modules

Abstract

We study projective and injective tensor products of Banach $$L^0$$ L 0 -modules over a $$\sigma $$ σ -finite measure space. En route, we extend to Banach $$L^0$$ L 0 -modules several technical tools of independent interest, such as quotient operators, summable families, and Schauder bases.