Lipschitz slices versus linear slices in Banach spaces
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- by Julio Becerra Guerrero, Ginés López-Pérez and Abraham Rueda Zoca PDF
- Proc. Amer. Math. Soc. 145 (2017), 1699-1708 Request permission
Abstract:
The aim of this note is to study the topology generated by Lipschitz slices in the unit sphere of a Banach space. We prove that the above topology agrees with the weak topology in the unit sphere and, as a consequence, we obtain easy Lipschitz characterizations of classical linear topics in Banach spaces as the Daugavet property, Radon-Nikodym property, convex point of continuity property and strong regularity, which shows that the above classical linear properties depend only on the natural uniformity in the Banach space given by the metric and the linear structure.References
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Additional Information
- Julio Becerra Guerrero
- Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
- Email: juliobg@ugr.es
- Ginés López-Pérez
- Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain – and – Instituto de Matemáticas de la Universidad de Granada (IEMath-GR)
- Email: glopezp@ugr.es
- Abraham Rueda Zoca
- Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
- MR Author ID: 1049318
- Email: arz0001@correo.ugr.es
- Received by editor(s): April 7, 2016
- Received by editor(s) in revised form: June 17, 2016
- Published electronically: October 13, 2016
- Additional Notes: The first author was partially supported by MEC (Spain) grant MTM2014-58984-P and Junta de Andalucía grants FQM-0199, FQM-1215.
The second author was partially supported by MINECO (Spain) grant MTM2015-65020-P and Junta de Andalucía grant FQM-185.
The third author was partially supported by Junta de Andalucía grants FQM-0199. - Communicated by: Thomas Schlumprecht
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1699-1708
- MSC (2010): Primary 46B20, 46B22
- DOI: https://doi.org/10.1090/proc/13372
- MathSciNet review: 3601560