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1997 | 125 | 2 | 179-186
Tytuł artykułu

Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that for every infinite-dimensional Banach space X with a Fréchet differentiable norm, the sphere $S_X$ is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessarily equivalent) $C^p$ norm (with $p ∈ ℕ ∪ {∞}$)$ is $C^p$ diffeomorphic to $Y \ {0}$.
Czasopismo
Rocznik
Tom
125
Numer
2
Strony
179-186
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-12-23
poprawiono
1997-03-11
Twórcy
  • Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense, Madrid, 28040, Spain, daniel@sunam1.mat.ucm.es
Bibliografia
  • [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.
  • [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.
  • [3] C. Bessaga and A. Pełczyński, Selected Topics in Infinite-Dimensional Topology, Monograf. Mat. 58, PWN, Warszawa, 1975.
  • [4] R. Deville, G. Godefroy and V. Zizler, Smoothness and Renormings in Banach Spaces, Pitman Monographs Surveys Pure and Appl. Math. 64, Longman, 1993.
  • [5] T. Dobrowolski, Smooth and R-analytic negligibility of subsets and extension of homeomorphisms in Banach spaces, Studia Math. 65 (1979), 115-139.
  • [6] T. Dobrowolski, Every infinite-dimensional Hilbert space is real-analytically isomorphic with its unit sphere, J. Funct. Anal. 134 (1995), 350-362.
  • [7] T. Dobrowolski, Relative classification of smooth convex bodies, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), 309-312.
  • [8] B. M. Garay, Cross-sections of solution funnels in Banach spaces, Studia Math. 97 (1990), 13-26.
  • [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.
  • [10] K. Goebel and J. Wośko, Making a hole in the space, Proc. Amer. Math. Soc. 114 (1992), 475-476.
  • [11] W. T. Gowers, A solution to Banach's hyperplane problem, Bull. London Math. Soc. 26 (1994), 523-530.
  • [12] W. T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874.
  • [13] R. C. James, Weakly compact sets, Trans. Amer. Math. Soc. 113 (1964), 129-140.
  • [14] K V. L. Klee, Convex bodies and periodic homeomorphisms in Hilbert space, ibid. 74 (1953), 10-43.
  • [15] S. Troyanski, On locally uniformly convex and differentiable norms in certain non-separable Banach spaces, Studia Math. 37 (1971), 173-180.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv125i2p179bwm
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