An almost nowhere Fréchet smooth norm on superreflexive spaces

Eva Matoušková

Studia Mathematica (1999)

  • Volume: 133, Issue: 1, page 93-99
  • ISSN: 0039-3223

Abstract

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Every separable infinite-dimensional superreflexive Banach space admits an equivalent norm which is Fréchet differentiable only on an Aronszajn null set.

How to cite

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Matoušková, Eva. "An almost nowhere Fréchet smooth norm on superreflexive spaces." Studia Mathematica 133.1 (1999): 93-99. <http://eudml.org/doc/216606>.

@article{Matoušková1999,
abstract = {Every separable infinite-dimensional superreflexive Banach space admits an equivalent norm which is Fréchet differentiable only on an Aronszajn null set.},
author = {Matoušková, Eva},
journal = {Studia Mathematica},
keywords = {Aronszajn null; convex; differentiable; Banach space; convex function; equivalent norm; Fréchet differentiable; superreflexive space; sparseness; Gateaux differentiability; Lipschitz function; superrefexive Banach space},
language = {eng},
number = {1},
pages = {93-99},
title = {An almost nowhere Fréchet smooth norm on superreflexive spaces},
url = {http://eudml.org/doc/216606},
volume = {133},
year = {1999},
}

TY - JOUR
AU - Matoušková, Eva
TI - An almost nowhere Fréchet smooth norm on superreflexive spaces
JO - Studia Mathematica
PY - 1999
VL - 133
IS - 1
SP - 93
EP - 99
AB - Every separable infinite-dimensional superreflexive Banach space admits an equivalent norm which is Fréchet differentiable only on an Aronszajn null set.
LA - eng
KW - Aronszajn null; convex; differentiable; Banach space; convex function; equivalent norm; Fréchet differentiable; superreflexive space; sparseness; Gateaux differentiability; Lipschitz function; superrefexive Banach space
UR - http://eudml.org/doc/216606
ER -

References

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  1. [A] N. Aronszajn, Differentiability of Lipschitzian mappings between Banach spaces, Studia Math. 57 (1976), 147-190. Zbl0342.46034
  2. [BL] Y. Benyamini and J. Lindenstrauss, Geometric non-linear functional analysis, to appear. Zbl0946.46002
  3. [C] M. Csörnyei, Aronszajn null and Gaussian null sets coincide, to appear. Zbl0952.46030
  4. [D] J. Diestel, Geometry of Banach Spaces, Springer, Berlin, 1975. Zbl0307.46009
  5. [K] P. L. Konyagin, On points of existence and nonuniqueness of elements of best approximation, in: Theory of Functions and its Applications, P. L. Ul'yanov (ed.), Izdat. Moskov. Univ., 1986, 38-43 (in Russian). 
  6. [Man] P. Mankiewicz, On the differentiability of Lipschitz mappings in Fréchet spaces, Studia Math. 45 (1973), 15-29. Zbl0219.46006
  7. [MM] J. Matoušek and E. Matoušková, A highly non-smooth norm on Hilbert space, Israel J. Math., to appear. Zbl0935.46012
  8. [M1] E. Matoušková, Convexity and Haar null sets, Proc. Amer. Math. Soc. 125 (1997), 1793-1799. Zbl0871.46005
  9. [M2] E. Matoušková, The Banach-Saks property and Haar null sets, Comment. Math. Univ. Carolin. 39 (1998), 71-80. Zbl0937.46011
  10. [PT] D. Preiss and J. Tišer, Two unexpected examples concerning differentiability of Lipschitz functions on Banach spaces, in: Geometric Aspects of Functional Analysis, Israel Seminar (GAFA), J. Lindenstrauss and V. Milman (eds.), Birkhäuser, 1995, 219-238. Zbl0872.46026
  11. [PZ] D. Preiss and L. Zajíček, Stronger estimates of smallness of sets of Fréchet nondifferentiability of convex functions, Suppl. Rend. Circ. Mat. Palermo (2) 3 (1984), 219-223. Zbl0547.46026

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