Some geometric properties of typical compact convex sets in Hilbert spaces

F. de Blasi

Displaying similar documents to “Some geometric properties of typical compact convex sets in Hilbert spaces”

On Typical Compact Convex Sets in Hilbert Spaces

De Blasi, F. (1997)

Serdica Mathematical Journal

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Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.

Properties of typical bounded closed convex sets in Hilbert space.

de Blasi, F.S., Zhivkov, N.V. (2005)

Abstract and Applied Analysis

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On spaces of measurable functions

C. Bessaga, A. Pełczyński (1972)

Studia Mathematica

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Dense families of continuous selections

E. Michael (1959)

Fundamenta Mathematicae

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Estimated extension theorem, homogeneous collections and skeletons and their applications to topological classification of linear metric spaces and convex sets

C. Bessaga, A. Pełczyński (1970)

Fundamenta Mathematicae

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Mappings into normed linear spaces

Victor Klee (1960)

Fundamenta Mathematicae

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Ambiguous loci of the farthest distance mapping from compact convex sets

F. De Blasi, J. Myjak (1995)

Studia Mathematica

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Let be a strictly convex separable Banach space of dimension at least 2. Let K() be the space of all nonempty compact convex subsets of endowed with the Hausdorff distance. Denote by $K^{0}$ the set of all X ∈ K() such that the farthest distance mapping $a \mapsto M_{X} (a)$ is multivalued on a dense subset of . It is proved that $K^{0}$ is a residual dense subset of K().

Some fixed point theorems

Barada Ray (1976)

Fundamenta Mathematicae

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The Space of Differences of Convex Functions on [0, 1]

Zippin, M. (2000)

Serdica Mathematical Journal

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∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany). The space K[0, 1] of differences of convex functions on the closed interval [0, 1] is investigated as a dual Banach space. It is proved that a continuous function f on [0, 1] belongs to K[0, 1] ...

On Bárány's theorems of Carathéodory and Helly type

Ehrhard Behrends (2000)

Studia Mathematica

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The paper begins with a self-contained and short development of Bárány’s theorems of Carathéodory and Helly type in finite-dimensional spaces together with some new variants. In the second half the possible generalizations of these results to arbitrary Banach spaces are investigated. The Carathéodory-Bárány theorem has a counterpart in arbitrary dimensions under suitable uniform compactness or uniform boundedness conditions. The proper generalization of the Helly-Bárány theorem reads...

On topological classification of complete linear metric spaces

C. Bessaga (1964)

Fundamenta Mathematicae

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An isomorphic Dvoretzky's theorem for convex bodies

Y. Gordon, O. Guédon, M. Meyer (1998)

Studia Mathematica

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We prove that there exist constants C>0 and 0 < λ < 1 so that for all convex bodies K in $ℝ^{n}$ with non-empty interior and all integers k so that 1 ≤ k ≤ λn/ln(n+1), there exists a k-dimensional affine subspace Y of $ℝ^{n}$ satisfying $d (Y \cap K, B_{2}^{k}) \leq C (1 + \sqrt (k / l n (n / (k l n (n + 1))))$ . This formulation of Dvoretzky’s theorem for large dimensional sections is a generalization with a new proof of the result due to Milman and Schechtman for centrally symmetric convex bodies. A sharper estimate holds for the n-dimensional simplex. ...