Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Hölder functions
HTML articles powered by AMS MathViewer
- by Stanislav Hencl PDF
- Proc. Amer. Math. Soc. 128 (2000), 3505-3511 Request permission
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
- Jan Malý and Luděk Zajíček, Approximate differentiation: Jarník points, Fund. Math. 140 (1991), no. 1, 87–97. MR 1139090, DOI 10.4064/fm-140-1-87-97
- L. Rodríguez-Piazza, Every separable Banach space is isometric to a space of continuous nowhere differentiable functions, Proc. Amer. Math. Soc. 123 (1995), no. 12, 3649–3654. MR 1328375, DOI 10.1090/S0002-9939-1995-1328375-8
- Andrew Bruckner, Differentiation of real functions, 2nd ed., CRM Monograph Series, vol. 5, American Mathematical Society, Providence, RI, 1994. MR 1274044, DOI 10.1090/crmm/005
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
- Received by editor(s): January 22, 1999
- Published electronically: May 18, 2000
- Communicated by: Dale Alspach
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1707147