A tree characterization of the point of continuity property in general Banach spaces
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- by Ginés López Pérez and José Antonio Soler Arias PDF
- Proc. Amer. Math. Soc. 140 (2012), 4243-4245 Request permission
Abstract:
We obtain a characterization of the point of continuity property for general bounded subsets in Banach spaces in terms of trees. For this we introduce the notion of a topologically weakly null tree and, as a consequence, we get that a general Banach space satisfies the point of continuity property if, and only if, every seminormalized topologically weakly null tree has a boundedly complete branch.References
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Additional Information
- Ginés López Pérez
- Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
- Email: glopezp@ugr.es
- José Antonio Soler Arias
- Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
- Email: jasoler@ugr.es
- Received by editor(s): February 18, 2011
- Received by editor(s) in revised form: March 9, 2011, April 11, 2011, May 23, 2011, and May 30, 2011
- Published electronically: April 17, 2012
- Additional Notes: This work was partially supported by MEC (Spain) Grant MTM2006-04837 and Junta de Andalucía Grants FQM-185 and Proyecto de Excelencia P06-FQM-01438.
- Communicated by: Thomas Schlumprecht
- © Copyright 2012 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 4243-4245
- MSC (2010): Primary 46B20, 46B22
- DOI: https://doi.org/10.1090/S0002-9939-2012-11281-X
- MathSciNet review: 2957215