The numerical radius Haagerup norm and Hilbert space square factorizations

Details The numerical radius Haagerup norm and Hilbert space square factorizations The numerical radius Haagerup norm and Hilbert space square factorizations

2004-04-07

arxiv.org/abs/math/0404152v1

Mathematics

Operator Algebras

16 pages

Scientific paper

We study a factorization of bounded linear maps from an operator space $A$ to its dual space $A^*$. It is shown that $T : A \longrightarrow A^*$ factors through a pair of a column Hilbert spaces $\mathcal{H}_c$ 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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