Abstract

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.

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Keywords

  • Proximinal
  • strongly proximinal
  • exposed face
  • norm attaining functional

Mathematics Subject Classification

46B20, 41A50, 41A65

References

  1. A. L. Garkavi: Helly’s problem and best approximation in spaces of continuous functions, Izv. Akad. Nauk SSSR, Ser. Mat. 31 (1967) 641–656.Google Scholar
  2. G. Godefroy, V. Indumathi: Proximinality in subspaces of c0, J. Approx. Theory 101 (1999) 175–181.https://doi.org/10.1006/jath.1999.3382Google Scholar
  3. G. Godefroy, V. Indumathi: Strong proximinality and polyhedral spaces, Rev. Mat. Complut. 14 (2001) 105–125.https://doi.org/10.5209/rev_REMA.2001.v14.n1.17047Google Scholar
  4. V. Indumathi: Proximinal subspaces of finite codimension in general normed linear spaces, Proc. Lond. Math. Soc., III. Ser. 45 (1982) 435–455.https://doi.org/10.1112/plms/s3-45.3.435Google Scholar
  5. E. Michael: Continuous selections. I, Ann. Math. 63 (1956) 361–382.https://doi.org/10.2307/1969615Google Scholar
  6. E. Michael: Selected selection theorems, Amer. Math. Monthly 63 (1956) 233–238.https://doi.org/10.1080/00029890.1956.11988794Google Scholar
  7. W. Rudin: Real and Complex Analysis, 3rd Ed., McGraw-Hill, New York (1987).Google Scholar
  8. I. Singer: Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer, Belrin (1970).https://doi.org/10.1007/978-3-662-41583-2Google Scholar

Suggested citation

V. Indumathi, S. Kalaiarasi. “Best Approximative Properties of Exposed Faces of C(Q).” Journal of Convex Analysis 24 (2017), No. 3, 959–967. https://doi.org/10.68381/jca24057

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press LLC.