Smooth Lipschitz Retractions of Starlike Bodies onto their Boundaries in Infinite‐Dimensional Banach Spaces | Zendy

Azagra Daniel | Zendy; Cepedello Boiso Manuel | Zendy

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Smooth Lipschitz Retractions of Starlike Bodies onto their Boundaries in Infinite‐Dimensional Banach Spaces

Author(s) -

Azagra Daniel,

Cepedello Boiso Manuel

Publication year - 2001

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1017/s0024609301008062

Subject(s) - lipschitz continuity , mathematics , banach space , contractible space , unit sphere , bounded function , lipschitz domain , norm (philosophy) , pure mathematics , mathematical analysis , political science , law

Let X be an infinite‐dimensional Banach space, and let A be a C p Lipschitz bounded starlike body (for instance the unit ball of a smooth norm). We prove that: the boundary ∂ A is C p Lipschitz contractible; there is a C p Lipschitz retraction from A onto ∂ A ; there is a C p Lipschitz map T : A → A with no approximate fixed points.

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