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Some geometric properties of typical compact convex sets in Hilbert spaces

F. de Blasi

Studia Mathematica (1999)

  • Volume: 135, Issue: 2, page 143-162
  • ISSN: 0039-3223

Abstract

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An investigation is carried out of the compact convex sets X in an infinite-dimensional separable Hilbert space , for which the metric antiprojection q X ( e ) from e to X has fixed cardinality n+1 ( n ⊆ ℕ arbitrary) for every e in a dense subset of . A similar study is performed in the case of the metric projection p X ( e ) from e to X where X is a compact subset of .

How to cite

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de Blasi, F.. "Some geometric properties of typical compact convex sets in Hilbert spaces." Studia Mathematica 135.2 (1999): 143-162. <http://eudml.org/doc/216647>.

@article{deBlasi1999,
abstract = {An investigation is carried out of the compact convex sets X in an infinite-dimensional separable Hilbert space , for which the metric antiprojection $q_X(e)$ from e to X has fixed cardinality n+1 ($n ⊆ ℕ$ arbitrary) for every e in a dense subset of . A similar study is performed in the case of the metric projection $p_X(e)$ from e to X where X is a compact subset of .},
author = {de Blasi, F.},
journal = {Studia Mathematica},
keywords = {Hilbert space; typical compact convex sets; typical compact sets; metric antiprojection; metric projection},
language = {eng},
number = {2},
pages = {143-162},
title = {Some geometric properties of typical compact convex sets in Hilbert spaces},
url = {http://eudml.org/doc/216647},
volume = {135},
year = {1999},
}

TY - JOUR
AU - de Blasi, F.
TI - Some geometric properties of typical compact convex sets in Hilbert spaces
JO - Studia Mathematica
PY - 1999
VL - 135
IS - 2
SP - 143
EP - 162
AB - An investigation is carried out of the compact convex sets X in an infinite-dimensional separable Hilbert space , for which the metric antiprojection $q_X(e)$ from e to X has fixed cardinality n+1 ($n ⊆ ℕ$ arbitrary) for every e in a dense subset of . A similar study is performed in the case of the metric projection $p_X(e)$ from e to X where X is a compact subset of .
LA - eng
KW - Hilbert space; typical compact convex sets; typical compact sets; metric antiprojection; metric projection
UR - http://eudml.org/doc/216647
ER -

References

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