Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces

Daniel Azagra

Studia Mathematica (1997)

  • Volume: 125, Issue: 2, page 179-186
  • ISSN: 0039-3223

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Azagra, Daniel. "Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces." Studia Mathematica 125.2 (1997): 179-186. <http://eudml.org/doc/216431>.

@article{Azagra1997,
abstract = {},
author = {Azagra, Daniel},
journal = {Studia Mathematica},
keywords = {$C^p$ smooth norm; spheres and hyperplanes in Banach spaces; infinite-dimensional Banach space; unit sphere; hyperplane; diffeomorphism},
language = {eng},
number = {2},
pages = {179-186},
title = {Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces},
url = {http://eudml.org/doc/216431},
volume = {125},
year = {1997},
}

TY - JOUR
AU - Azagra, Daniel
TI - Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces
JO - Studia Mathematica
PY - 1997
VL - 125
IS - 2
SP - 179
EP - 186
AB -
LA - eng
KW - $C^p$ smooth norm; spheres and hyperplanes in Banach spaces; infinite-dimensional Banach space; unit sphere; hyperplane; diffeomorphism
UR - http://eudml.org/doc/216431
ER -

References

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  1. [1] C. Bessaga, Every infinite-dimensional Hilbert space is diffeomorphic with its unit sphere, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 14 (1966), 27-31. Zbl0151.17703
  2. [2] C. Bessaga, Interplay between infinite-dimensional topology and functional analysis. Mappings defined by explicit formulas and their applications, Topology Proc. 19 (1994), 15-35. Zbl0840.46008
  3. [3] C. Bessaga and A. Pełczyński, Selected Topics in Infinite-Dimensional Topology, Monograf. Mat. 58, PWN, Warszawa, 1975. 
  4. [4] R. Deville, G. Godefroy and V. Zizler, Smoothness and Renormings in Banach Spaces, Pitman Monographs Surveys Pure and Appl. Math. 64, Longman, 1993. Zbl0782.46019
  5. [5] T. Dobrowolski, Smooth and R-analytic negligibility of subsets and extension of homeomorphisms in Banach spaces, Studia Math. 65 (1979), 115-139. Zbl0421.46012
  6. [6] T. Dobrowolski, Every infinite-dimensional Hilbert space is real-analytically isomorphic with its unit sphere, J. Funct. Anal. 134 (1995), 350-362. Zbl0869.46013
  7. [7] T. Dobrowolski, Relative classification of smooth convex bodies, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), 309-312. Zbl0354.58005
  8. [8] B. M. Garay, Cross-sections of solution funnels in Banach spaces, Studia Math. 97 (1990), 13-26. Zbl0714.34099
  9. [9] B. M. Garay, Deleting homeomorphisms and the failure of Peano's existence theorem in infinite-dimensional Banach spaces, Funkcial. Ekvac. 34 (1991), 85-93. Zbl0734.34055
  10. [10] K. Goebel and J. Wośko, Making a hole in the space, Proc. Amer. Math. Soc. 114 (1992), 475-476. Zbl0747.46011
  11. [11] W. T. Gowers, A solution to Banach's hyperplane problem, Bull. London Math. Soc. 26 (1994), 523-530. Zbl0838.46011
  12. [12] W. T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874. Zbl0827.46008
  13. [13] R. C. James, Weakly compact sets, Trans. Amer. Math. Soc. 113 (1964), 129-140. Zbl0129.07901
  14. [14] K V. L. Klee, Convex bodies and periodic homeomorphisms in Hilbert space, ibid. 74 (1953), 10-43. Zbl0050.33202
  15. [15] S. Troyanski, On locally uniformly convex and differentiable norms in certain non-separable Banach spaces, Studia Math. 37 (1971), 173-180. Zbl0214.12701

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