Construction of pathological Gâteaux differentiable functions
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- by Robert Deville, Milen Ivanov and Sebastián Lajara
- Proc. Amer. Math. Soc. 143 (2015), 129-139
- DOI: https://doi.org/10.1090/S0002-9939-2014-12206-4
- Published electronically: August 15, 2014
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Abstract:
We prove that for many pairs $(X,Y)$ of classical Banach spaces, there exists a bounded, Lipschitz, Gâteaux differentiable function from $X$ to $Y$ whose derivatives are all far apart.References
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Bibliographic Information
- Robert Deville
- Affiliation: Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351, cours de la Libération, 33400 Talence, France
- Email: Robert.Deville@math.u-bordeaux1.fr
- Milen Ivanov
- Affiliation: Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Boulevard, 1164 Sofia, Bulgaria
- Email: milen@fmi.uni-sofia.bg
- Sebastián Lajara
- Affiliation: Departamento de Matemáticas, Escuela de Ingenieros Industriales, Universidad de Castilla-La Mancha, Campus Universitario, 02071 Albacete, Spain
- MR Author ID: 739008
- Email: Sebastian.Lajara@uclm.es
- Received by editor(s): July 10, 2012
- Received by editor(s) in revised form: January 14, 2013, and February 13, 2013
- Published electronically: August 15, 2014
- Additional Notes: The second author was partially supported by NIS-SU, contract No. 133/2012.
The third author was partialy supported by MTM2011-25377 (Ministerio de Ciencia e Innovación) and by JCCM PEII11-0132-7661. - Communicated by: Thomas Schlumprecht
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 129-139
- MSC (2010): Primary 46B20, 46G05; Secondary 46T20
- DOI: https://doi.org/10.1090/S0002-9939-2014-12206-4
- MathSciNet review: 3272738