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Simultaneous approximation and interpolation in $ l\sb{1}$


Author: Joseph M. Lambert
Journal: Proc. Amer. Math. Soc. 32 (1972), 150-152
MSC: Primary 41A65
DOI: https://doi.org/10.1090/S0002-9939-1972-0291706-9
MathSciNet review: 0291706
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Abstract: In a recent paper of R. Holmes and J. Lambert a geometrical approach was taken to the property of simultaneous approximation and interpolation which is norm preserving (SAIN), first introduced by F. Deutsch and P. Morris. An open question in both papers was if M is the subspace of $ {l_1}$ consisting of the elements having only finitely many nonzero components does the triple $ ({l_1},M,G)$ have property SAIN for all finite dimensional subspaces G contained in $ {l_\infty }$. This question is answered affirmatively by use of a generalization of Yamabe's theorem extending Helly's theorem.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0291706-9
Keywords: Abstract approximation, approximation and interpolation, norm preserving approximation, Helly's theorem, Yamabe's theorem
Article copyright: © Copyright 1972 American Mathematical Society

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