×

zbMATH — the first resource for mathematics

Interplay between infinite-dimensional topology and functional analysis. Mappings defined by explicit formulas and their applications. (English) Zbl 0840.46008
Summary: We recall some explicit formulas of analytic character which were invented during the process of formation of infinite-dimensional topology, and present some applications of them. The following topics are covered:
A. Radial homeomorphisms and retractions of convex bodies; analogues of gauge functionals and radial retractions for Banach lattices. Applications: Lipschitz retraction onto \(c_0\) (Lindenstrauss) and lack of fixed points for Lipschitz self-maps of non compact convex sets (Lin-Sternfeld).
B. Non-complete-norm deleting homeomorphisms and diffeomorphisms with applications
(Garay) to ordinary differential equations. An analogy with West’s theorem on fixed point sets of transformation groups.
C. The coordinate switching technique: a “simultaneous” proof of West’s theorem and the Ribe-Aharoni-Lindenstrauss example of uniformly homeomorphic and not Lipschitz homeomorphic separable Banach spaces.

MSC:
46B20 Geometry and structure of normed linear spaces
46B42 Banach lattices
58C30 Fixed-point theorems on manifolds
52A07 Convex sets in topological vector spaces (aspects of convex geometry)
PDF BibTeX XML Cite
Full Text: Link