Numerical radius Haagerup norm and square factorization through Hilbert spaces

摘要

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 H_c and its dual space if and only if T is a bounded linear form on A directX 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.