This is an announcement for the paper "The numerical radius Haagerup norm and Hilbert space square factorizations" by Takashi Itoh and Masaru Nagisa.

Abstract: We study a factorization of bounded linear maps from an operator space $A$ to its dual space $A^*$. It is shown that $T : A \longrightarrow A^*$ 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.

Archive classification: Operator Algebras

Mathematics Subject Classification: 46L07 (Primary) 47L25, 46B28, 46L06 (Secontary)

Remarks: 16 pages

The source file(s), ina03.tex: 44003 bytes, is(are) stored in gzipped form as 0404152.gz with size 12kb. The corresponding postcript file has gzipped size 70kb.

Submitted from: itoh@edu.gunma-u.ac.jp

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