Numerical radius Haagerup norm and square factorization through Hilbert spaces

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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

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 58(2), 363-377, 2006-04-01

    The Mathematical Society of Japan

References:  24

Codes

  • NII Article ID (NAID)
    10018381245
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    7892100
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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