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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 | References | Similar Articles | Additional Information


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 $f$.

References [Enhancements On Off] (What's this?)

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Additional Information

Angel Rodriguez Palacios
Affiliation: Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain

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

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