Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Continuous metric projections
HTML articles powered by AMS MathViewer

by Joseph M. Lambert PDF
Proc. Amer. Math. Soc. 48 (1975), 179-184 Request permission

Abstract:

An example is given of a reflexive, rotund Banach space whose dual space is not Fréchet differentiable such that every metric projection onto closed subspaces is norm continuous. This example shows that several published conjectures on necessary and sufficient conditions for a reflexive, rotund Banach space to have norm continuous metric projections onto all closed subspaces are incorrect.
References
  • E. W. Cheney and D. E. Wulbert, The existence and unicity of best approximations, Math. Scand. 24 (1969), 113–140. MR 261241, DOI 10.7146/math.scand.a-10925
  • Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
  • Richard B. Holmes, A course on optimization and best approximation, Lecture Notes in Mathematics, Vol. 257, Springer-Verlag, Berlin-New York, 1972. MR 0420367
  • R. B. Holmes, On the continuity of best approximation operators, Symposium on Infinite-Dimensional Topology (Louisiana State Univ., Baton Rouge, La., 1967) Ann. of Math. Studies, No. 69, Princeton Univ. Press, Princeton, N. J., 1972, pp. 137–157. MR 0404959
  • Richard Holmes and Bernard Kripke, Smoothness of approximation, Michigan Math. J. 15 (1968), 225–248. MR 228904
  • V. Klee, Two renorming constructions related to a question of Anselone, Studia Math. 33 (1969), 231–242. MR 248504, DOI 10.4064/sm-33-2-231-242
  • E. B. Ošman, The continuity of metric projection onto certain classes of subspaces in a Banach space, Dokl. Akad. Nauk SSSR 195 (1970), 555–557 (Russian). MR 0273372
Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 48 (1975), 179-184
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0358186-9
  • MathSciNet review: 0358186