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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
DOI: https://doi.org/10.1090/S0002-9939-00-05595-7
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.


References [Enhancements On Off] (What's this?)

  • 1. J. Malý and L. Zajícek, Approximate differentiation: Jarník points, Fund. Math. 140 (1991), 87-97. MR 92m:26006
  • 2. L. Rodriguez-Piazza, Every separable Banach space is isometric to a space of continuous nowhere differentiable functions, Proc. Amer. Math. Soc. 123 (1995), 3649-3654. MR 96d:46007
  • 3. A. Bruckner, Differentation of Real Functions, CRM Monograph Series, Volume 5 [2nd edition], Providence, Rhode Island, 1994. MR 94m:26001

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

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