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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Hölder functions


Author: Stanislav Hencl
Journal: Proc. Amer. Math. Soc. 128 (2000), 3505-3511
MSC (1991): Primary 26A27, 46B04
Published electronically: May 18, 2000
MathSciNet review: 1707147
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Abstract: The well-known Banach-Mazur theorem says that every separable Banach space can be isometrically embedded into $C([ 0,1])$. We prove that this embedding can have the property that the image of each nonzero element is a nowhere approximatively differentiable and nowhere Hölder function. It improves a recent result of L. Rodriguez-Piazza where the images are nowhere differentiable functions.


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Additional Information

Stanislav Hencl
Affiliation: Department of Mathematical Analysis, Charles University, Sokolovska 83, 186 00 Prague 8, Czech Republic
Email: Hencl@karlin.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05595-7
PII: S 0002-9939(00)05595-7
Received by editor(s): January 22, 1999
Published electronically: May 18, 2000
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society