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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.