[Banach] Abstract of a paper by Takashi Itoh and Masaru Nagisa

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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