Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces

• Autorzy: Daniel Azagra
• 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 $Y \ {0}$.

Słowa kluczowe

EN

$C^p$ smooth norm; spheres and hyperplanes in Banach spaces

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 58B99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 125
• Numer: 2
• Strony: 179-186

Daty

wydano

1997

otrzymano

1996-12-23

poprawiono

1997-03-11

Twórcy

autor

Daniel Azagra

• Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense, Madrid, 28040, Spain,

Bibliografia

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