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1

Bootstrapping Kirszbraun's extension theorem

100%

Kopecká E.

Fundamenta Mathematicae

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2012

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tom 217

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nr 1

13-19

EN

We show how Kirszbraun's theorem on extending Lipschitz mappings in Hilbert space implies its own generalization. There is a continuous extension operator preserving the Lipschitz constant of every mapping.

2

A product of three projections

63%

Kopecká E., Müller V.

Studia Mathematica

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2014

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tom 223

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nr 2

175-186

EN

Let X and Y be two closed subspaces of a Hilbert space. If we send a point back and forth between them by orthogonal projections, the iterates converge to the projection of the point onto the intersection of X and Y by a theorem of von Neumann. Any sequence of orthoprojections of a point in a Hilbert space onto a finite family of closed subspaces converges weakly, according to Amemiya and Ando. The problem of norm convergence was open for a long time. Recently Adam Paszkiewicz constructed five subspaces of an infinite-dimensional Hilbert space and a sequence of projections on them which does not converge in norm. We construct three such subspaces, resolving the problem fully. As a corollary we observe that the Lipschitz constant of a certain Whitney-type extension does in general depend on the dimension of the underlying space.

3

Nonexpansive retracts in Banach spaces

63%

Kopecká E., Reich S.

Banach Center Publications

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2007

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tom 77

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nr 1

161-174

EN

We study various aspects of nonexpansive retracts and retractions in certain Banach and metric spaces, with special emphasis on the compact nonexpansive envelope property.

Ograniczanie wyników

1 Banach Center Publications

1 Fundamenta Mathematicae

1 Studia Mathematica

3 Kopecká E.

1 Müller V.

1 Reich S.

1 2014

1 2012

1 2007

Bootstrapping Kirszbraun's extension theorem

A product of three projections

Nonexpansive retracts in Banach spaces