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Spring 2009 Hilbertian matrix cross normed spaces arising from normed ideals
Takahiro Ohta
Illinois J. Math. 53(1): 1-24 (Spring 2009). DOI: 10.1215/ijm/1264170836


Generalizing Pisier’s idea, we introduce a Hilbertian matrix cross normed space associated with a pair of symmetric normed ideals. When the two ideals coincide, we show that our construction gives an operator space if and only if the ideal is the Schatten class. In general, a pair of symmetric normed ideals that are not necessarily the Schatten class may give rise to an operator space. We study the space of completely bounded mappings between the matrix cross normed spaces obtained in this way and show that the multiplicator norm naturally appears as the completely bounded norm.


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Takahiro Ohta. "Hilbertian matrix cross normed spaces arising from normed ideals." Illinois J. Math. 53 (1) 1 - 24, Spring 2009.


Published: Spring 2009
First available in Project Euclid: 22 January 2010

zbMATH: 1187.47059
MathSciNet: MR2584932
Digital Object Identifier: 10.1215/ijm/1264170836

Primary: 47L20 , 47L25

Rights: Copyright © 2009 University of Illinois at Urbana-Champaign


Vol.53 • No. 1 • Spring 2009
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