Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections
A number of semicontinuity concepts and the relations between them are discussed. Characterizations are given for when the (set-valued) metric projection PM onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. A geometric characteriza...
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| Veröffentlicht in: | Journal of approximation theory 2002-03, Vol.115 (1), p.120-143 |
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| container_end_page | 143 |
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| container_issue | 1 |
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| container_title | Journal of approximation theory |
| container_volume | 115 |
| creator | Brown, A.L. Deutsch, Frank Indumathi, V. Kenderov, Petar S. |
| description | A number of semicontinuity concepts and the relations between them are discussed. Characterizations are given for when the (set-valued) metric projection PM onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. A geometric characterization is given of those normed linear spaces X such that the metric projection onto every one-dimensional subspace has a continuous C0(T) and L1(μ) that have this property are determined. |
| doi_str_mv | 10.1006/jath.2001.3654 |
| format | Article |
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Characterizations are given for when the (set-valued) metric projection PM onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. 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Characterizations are given for when the (set-valued) metric projection PM onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. A geometric characterization is given of those normed linear spaces X such that the metric projection onto every one-dimensional subspace has a continuous C0(T) and L1(μ) that have this property are determined.</abstract><pub>Elsevier Inc</pub><doi>10.1006/jath.2001.3654</doi><tpages>24</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of approximation theory, 2002-03, Vol.115 (1), p.120-143 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | approximate lower semicontinuity best approximation continuous selection derived mapping geometry of Banach spaces lower semicontinuity Lp-space metric projection set valued mapping space of continuous functions weak lower semicontinuity |
| title | Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections |
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