Journal of Convex Analysis 24 (2017), No. 3, 959--967
Copyright Heldermann Verlag 2017
Best Approximative Properties of Exposed Faces of C(Q)
V. Indumathi
Dept. of Mathematics, Pondicherry University, Pondicherry 605014, India
pdyindumath@gmail.com
S. Kalaiarasi
Dept. of Mathematics, Pondicherry University, Pondicherry 605014, India
kalaiarasi.math@gmail.com
If C is an exposed face of the unit sphere of the Banach space C(Q), Q a compact Hausdorff space, then the closed convex set C is strongly proximinal and the metric projection onto C is Hausdorff metric continuous.
Keywords: Proximinal, strongly proximinal, exposed face, norm attaining functional.
MSC: 46B20, 41A50, 41A65
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