This article is cited in 2 papers

Weak continuity of metric projections

V. S. Balaganskii

Institute of Mathematics and Mechanics, Ural Scientific Center of the AS of USSR

Abstract: A necessary and sufficient condition is found for weak continuity of a metric projection onto a finite-dimensional subspace in $l_p$ ($1<p\ne2$). A metric projection onto a boundedly compact set in $l_p$ is sequentially weakly upper semicontinueus. An example is given on a convex, compact set in $l_2$ onto which the metric projection is not weakly continuous.

UDC: 517.5

Received: 29.06.1976

 English version: Mathematical Notes, 1977, 22:3, 681–687

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