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Proceedings of the American Mathematical Society

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



Continuous metric projections

Author: Joseph M. Lambert
Journal: Proc. Amer. Math. Soc. 48 (1975), 179-184
MathSciNet review: 0358186
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Abstract | References | Additional Information

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.

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Additional Information

Keywords: Abstract approximation, metric projections, best approximation maps
Article copyright: © Copyright 1975 American Mathematical Society