Numerical radius Haagerup norm and square factorization through Hilbert spaces

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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.

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