Simultaneous approximation and interpolation in $l_{1}$
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- by Joseph M. Lambert PDF
- Proc. Amer. Math. Soc. 32 (1972), 150-152 Request permission
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.References
- Frank Deutsch and Peter D. Morris, On simultaneous approximation and interpolation which preserves the norm, J. Approximation Theory 2 (1969), 355–373. MR 252931, DOI 10.1016/0021-9045(69)90004-5
- Richard Holmes and Joseph Lambert, A geometrical approach to property (SAIN), J. Approximation Theory 7 (1973), 132–142. MR 344769, DOI 10.1016/0021-9045(73)90060-9
- Joram Lindenstrauss, On extreme points in $l_{1}$, Israel J. Math. 4 (1966), 59–61. MR 200701, DOI 10.1007/BF02760071
- Hidehiko Yamabe, On an extension of the Helly’s theorem, Osaka Math. J. 2 (1950), 15–17. MR 39914
Additional Information
- © Copyright 1972 American Mathematical Society
- 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