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Bulletin of the London Mathematical Society Advance Access published online on April 1, 2008
Bulletin of the London Mathematical Society, doi:10.1112/blms/bdm113
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© 2008 London Mathematical Society

Banach spaces with polynomial numerical index 1

Han Ju Lee

Mathematics Department
202 Mathematical Science Building
University of Missouri
Columbia, MO 65211
USA

Received 24 January 2007. Revision received 27 July 2007.

We characterize Banach spaces with polynomial numerical index 1 when they have the Radon–Nikodym property. The holomorphic numerical index is introduced and the characterization of the Banach space with holomorphic numerical index 1 is obtained when it has the Radon–Nikodym property.

2000 Mathematics Subject Classification 46G25 (primary), 46B20, 46B22 (secondary).

This work was supported by the Korea Research FoundationGrant funded by the Korean Government(MOEHRD) (KRF-2006-352-C00003) and by grant No. R01-2004-000-10055-0 from the Basic Research Program of the Korea Science & Engineering Foundation.


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