Numerical radius Haagerup norm and square factorization through Hilbert spaces

Abstract

We study a factorization of bounded linear maps from an operator space A to its dual space A^*. It is shown that T: A→A^* factors through a pair of column Hilbert space $¥mathscr{H}$_c and its dual space if and only if T is a bounded linear form on A$¥otimes$A by the canonical identification equipped with a numerical radius type Haagerup norm. As a consequence, we characterize a bounded linear map from a Banach space to its dual space, which factors through a pair of Hilbert spaces.