The dual of the space of bounded operators on a Banach space

Abstract

Given Banach spaces X and Y, we ask about the dual space of the 𝒧(X, Y). This paper surveys results on tensor products of Banach spaces with the main objective of describing the dual of spaces of bounded operators. In several cases and under a variety of assumptions on X and Y, the answer can best be given as the projective tensor product of X** and Y*.

Keywords

• tensor products
• dual spaces
• dual of spaces of operators
• primary 46b78
• secondary 46b10