On a sufficient condition for proximity
Author:
Ka Sing Lau
Journal:
Trans. Amer. Math. Soc. 251 (1979), 343356
MSC:
Primary 46B99; Secondary 41A65, 47D15
MathSciNet review:
531983
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Abstract: A closed subspace M in a Banach space X is called Uproximinal if it satisfies: , for some positive valued function , , and as , where S is the closed unit ball of X. One of the important properties of this class of subspaces is that the metric projections are continuous. We show that many interesting subspaces are Uproximinal, for example, the subspaces with the 2ball property (semi Mideals) and certain subspaces of compact operators in the spaces of bounded linear operators.
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 R. Holmes, B. Scranton and J. Ward, Approximation from the space of compact operators and other Mideals, Duke Math. J. 42 (1975), 259269. MR 0394301 (52:15104)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197905319830
PII:
S 00029947(1979)05319830
Keywords:
Compact operators,
measurable functions,
Mideals,
proximity,
uniformly convex
Article copyright:
© Copyright 1979
American Mathematical Society
