Numerical radius Haagerup norm and square factorization through Hilbert spaces
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- Itoh Takashi ITOH Takashi
- Department of Mathematics Gunma University
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- Nagisa Masaru NAGISA Masaru
- Department of Mathematics and Informatics Chiba University
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Author(s)
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- Itoh Takashi ITOH Takashi
- Department of Mathematics Gunma University
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- Nagisa Masaru NAGISA Masaru
- Department of Mathematics and Informatics Chiba University
Abstract
We study a factorization of bounded linear maps from an operator space <i>A</i> to its dual space <i>A</i><sup>*</sup>. It is shown that <i>T</i>: <i>A</i>→<i>A</i><sup>*</sup> factors through a pair of column Hilbert space $¥mathscr{H}$<sub><i>c</i></sub> and its dual space if and only if <i>T</i> is a bounded linear form on <i>A</i>$¥otimes$<i>A</i> 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.
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 58(2), 363-377, 2006-04-01
The Mathematical Society of Japan
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