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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Numerical index and renorming


Authors: Catherine Finet, Miguel Martín and Rafael Payá
Journal: Proc. Amer. Math. Soc. 131 (2003), 871-877
MSC (2000): Primary 46B20, 47A12
Published electronically: August 19, 2002
MathSciNet review: 1937425
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Abstract: We study the numerical index of a Banach space from the isomorphic point of view, that is, we investigate the values of the numerical index which can be obtained by renorming the space. The set of these values is always an interval which contains $[0,1/3[$ in the real case and $[e^{-1},1/2[$ in the complex case. Moreover, for ``most'' Banach spaces the least upper bound of this interval is as large as possible, namely $1$.


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Additional Information

Catherine Finet
Affiliation: Institut de Mathématique et d’Informatique, Université de Mons-Hainaut, Avenue du champ de mars 8, B-7000 Mons, Belgium
Email: catherine.finet@umh.ac.be

Miguel Martín
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Email: mmartins@ugr.es

Rafael Payá
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Email: rpaya@ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06576-0
PII: S 0002-9939(02)06576-0
Keywords: Numerical range, numerical index, renorming
Received by editor(s): May 29, 2001
Received by editor(s) in revised form: October 18, 2001
Published electronically: August 19, 2002
Additional Notes: The first author was partially supported by La Banque Nationale de Belgique
The second and third authors were partially supported by Spanish MCYT project no. BFM2000-1467
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2002 American Mathematical Society