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April, 2006 Numerical radius Haagerup norm and square factorization through Hilbert spaces
Takashi ITOH, Masaru NAGISA
J. Math. Soc. Japan 58(2): 363-377 (April, 2006). DOI: 10.2969/jmsj/1149166780


We study a factorization of bounded linear maps from an operator space A to its dual space A * . It is shown that $T: A \rightarrow A*$ factors through a pair of column Hilbert space c and its dual space if and only if T is a bounded linear form on A 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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Takashi ITOH. Masaru NAGISA. "Numerical radius Haagerup norm and square factorization through Hilbert spaces." J. Math. Soc. Japan 58 (2) 363 - 377, April, 2006.


Published: April, 2006
First available in Project Euclid: 1 June 2006

zbMATH: 1105.46038
MathSciNet: MR2228564
Digital Object Identifier: 10.2969/jmsj/1149166780

Primary: 46L07
Secondary: 46B28 , 47L05 , 47L25

Keywords: $C^*$-algebra , completely bounded map , factorization through Hilbert spaces , numerical radius Haagerup norm , operator space

Rights: Copyright © 2006 Mathematical Society of Japan


Vol.58 • No. 2 • April, 2006
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