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

 

A numerical range characterization of uniformly smooth Banach spaces


Author: Angel Rodriguez Palacios
Journal: Proc. Amer. Math. Soc. 129 (2001), 815-821
MSC (2000): Primary 46B04, 46B20
Published electronically: September 19, 2000
MathSciNet review: 1706989
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Abstract:

We prove that a Banach space $X$ is uniformly smooth if and only if, for every $X$-valued bounded function $f$ on the unit sphere of $X$, the intrinsic numerical range of $f$ is equal to the closed convex hull of the spatial numerical range of $f$.


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Additional Information

Angel Rodriguez Palacios
Affiliation: Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain
Email: apalacio@goliat.ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05621-5
PII: S 0002-9939(00)05621-5
Received by editor(s): October 19, 1998
Received by editor(s) in revised form: May 24, 1999
Published electronically: September 19, 2000
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society