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Construction of pathological Gâteaux differentiable functions


Authors: Robert Deville, Milen Ivanov and Sebastián Lajara
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
Published electronically: August 15, 2014
MathSciNet review: 3272738
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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.


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Additional 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
Email: Sebastian.Lajara@uclm.es

DOI: https://doi.org/10.1090/S0002-9939-2014-12206-4
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.