A numerical range characterization of uniformly smooth Banach spaces
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- by Angel Rodriguez Palacios PDF
- Proc. Amer. Math. Soc. 129 (2001), 815-821 Request permission
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 $f$.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 815-821
- MSC (2000): Primary 46B04, 46B20
- DOI: https://doi.org/10.1090/S0002-9939-00-05621-5
- MathSciNet review: 1706989