Analytic and C k approximations of norms in separable Banach spaces

Robert Deville; Vladimir Fonf; Petr Hájek

Studia Mathematica (1996)

  • Volume: 120, Issue: 1, page 61-74
  • ISSN: 0039-3223

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Deville, Robert, Fonf, Vladimir, and Hájek, Petr. "Analytic and $C^k$ approximations of norms in separable Banach spaces." Studia Mathematica 120.1 (1996): 61-74. <http://eudml.org/doc/216321>.

@article{Deville1996,
abstract = {},
author = {Deville, Robert, Fonf, Vladimir, Hájek, Petr},
journal = {Studia Mathematica},
keywords = {analytic norm; approximation; convex function; geometry of Banach spaces; every equivalent norm can be approximated uniformly on bounded sets by analytic norms; -smooth norms},
language = {eng},
number = {1},
pages = {61-74},
title = {Analytic and $C^k$ approximations of norms in separable Banach spaces},
url = {http://eudml.org/doc/216321},
volume = {120},
year = {1996},
}

TY - JOUR
AU - Deville, Robert
AU - Fonf, Vladimir
AU - Hájek, Petr
TI - Analytic and $C^k$ approximations of norms in separable Banach spaces
JO - Studia Mathematica
PY - 1996
VL - 120
IS - 1
SP - 61
EP - 74
AB -
LA - eng
KW - analytic norm; approximation; convex function; geometry of Banach spaces; every equivalent norm can be approximated uniformly on bounded sets by analytic norms; -smooth norms
UR - http://eudml.org/doc/216321
ER -

References

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  1. [D] R. Deville, Geometrical implications of the existence of very smooth bump functions in Banach spaces, Israel J. Math. 6 (1989), 1-22. Zbl0691.46009
  2. [DFH] R. Deville, V. Fonf and P. Hájek, Analytic and polyhedral approximation of convex bodies in separable polyhedral Banach spaces, to appear. Zbl0920.46011
  3. [DGZ] R. Deville, G. Godefroy and V. Zizler, Smoothness and Renormings in Banach Spaces, Pitman Monographs Surveys Pure Appl. Math. 64, Longman, 1993. 
  4. [Dieu] J. Dieudonné, Foundations of Modern Analysis, Academic Press, New York, 1960. Zbl0100.04201
  5. [FFWZ] M. Fabian, D. Preiss, J. H. M. Whitfield and V. Zizler, Separating polynomials on Banach spaces, Quart. J. Math. Oxford Ser. (2) 40 (1989), 409-422. Zbl0715.46007
  6. [Fe] H. Federer, Geometric Measure Theory, Springer, 1969. 
  7. [HH] P. Habala and P. Hájek, Stabilization of polynomials, C. R. Acad. Sci. Paris Sér. I 320 (1995), 821-825. Zbl0826.46037
  8. [H1] R. Haydon, Normes infiniment différentiables sur certains espaces de Banach, ibid. 315 (1992), 1175-1178. Zbl0788.46008
  9. [H2] R. Haydon, Smooth functions and partitions of unity on certain Banach spaces, to appear. 
  10. [Ku1] J. Kurzweil, On approximation in real Banach spaces, Studia Math. 14 (1954), 213-231. 
  11. [Ku2] J. Kurzweil, On approximation in real Banach spaces by analytic operations, ibid. 16 (1957), 124-129. Zbl0080.32602
  12. [M] P. Mazet, Analytic Sets in Locally Convex Spaces, North-Holland Math. Stud. 89, North-Holland, 1984. 
  13. [N] L. Nachbin, Topology on Spaces of Holomorphic Mappings, Springer, 1969. Zbl0172.39902
  14. [NS] A. M. Nemirovskiĭ and S. M. Semenov, On polynomial approximation of functions on Hilbert space, Mat. Sb. 92 (1973), 257-281 (in Russian). Zbl0286.41025
  15. [Zp] M. Zippin, The separable extension problem, Israel J. Math. 26 (1977), 372-387. Zbl0347.46076

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