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Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces

100%

Azagra D.

Studia Mathematica

1997

tom 125

nr 2

179-186

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 $Y \ {0}$.

On diffeomorphisms deleting weak compacta in Banach spaces

63%

Azagra D., Montesinos A.

Studia Mathematica

2004

tom 162

nr 3

229-244

We prove that if X is an infinite-dimensional Banach space with $C^{p}$ smooth partitions of unity then X and X∖ K are $C^{p}$ diffeomorphic for every weakly compact set K ⊂ X.

Ograniczanie wyników

2 Studia Mathematica

2 Azagra D.

1 Montesinos A.

1 2004

1 1997

Wyniki wyszukiwania

Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces

On diffeomorphisms deleting weak compacta in Banach spaces