# 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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topDeville, 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

top- [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
- [DFH] R. Deville, V. Fonf and P. Hájek, Analytic and polyhedral approximation of convex bodies in separable polyhedral Banach spaces, to appear. Zbl0920.46011
- [DGZ] R. Deville, G. Godefroy and V. Zizler, Smoothness and Renormings in Banach Spaces, Pitman Monographs Surveys Pure Appl. Math. 64, Longman, 1993.
- [Dieu] J. Dieudonné, Foundations of Modern Analysis, Academic Press, New York, 1960. Zbl0100.04201
- [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
- [Fe] H. Federer, Geometric Measure Theory, Springer, 1969.
- [HH] P. Habala and P. Hájek, Stabilization of polynomials, C. R. Acad. Sci. Paris Sér. I 320 (1995), 821-825. Zbl0826.46037
- [H1] R. Haydon, Normes infiniment différentiables sur certains espaces de Banach, ibid. 315 (1992), 1175-1178. Zbl0788.46008
- [H2] R. Haydon, Smooth functions and partitions of unity on certain Banach spaces, to appear.
- [Ku1] J. Kurzweil, On approximation in real Banach spaces, Studia Math. 14 (1954), 213-231.
- [Ku2] J. Kurzweil, On approximation in real Banach spaces by analytic operations, ibid. 16 (1957), 124-129. Zbl0080.32602
- [M] P. Mazet, Analytic Sets in Locally Convex Spaces, North-Holland Math. Stud. 89, North-Holland, 1984.
- [N] L. Nachbin, Topology on Spaces of Holomorphic Mappings, Springer, 1969. Zbl0172.39902
- [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
- [Zp] M. Zippin, The separable extension problem, Israel J. Math. 26 (1977), 372-387. Zbl0347.46076

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