On proximinality in $L_{1}(T\times S)$
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- by S. M. Holland, W. A. Light and L. J. Sulley PDF
- Proc. Amer. Math. Soc. 86 (1982), 279-282 Request permission
Abstract:
It is proved that if $G$ and $H$ are finite-dimensional subspaces of ${L_1}(S)$ and ${L_1}(T)$ respectively then each element of ${L_1}(T \times S)$ has a best approximation in the subspace ${L_1}(T) \otimes G + H \otimes {L_1}(S)$.References
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E. W. Cheney, J. H. McCabe, W. A. Light and G. Phillips, The approximation of bivariate functions by sums of univariate ones using the ${L_1}$-metric, Center for Numerical Analysis Technical Report, University of Texas, 1979.
N. Dunford and J. T. Schwartz, Linear operators, Part 1, Interscience, New York, 1959.
- W. A. Light and E. W. Cheney, Some best-approximation theorems in tensor-product spaces, Math. Proc. Cambridge Philos. Soc. 89 (1981), no. 3, 385–390. MR 602291, DOI 10.1017/S0305004100058278
- J. R. Respess Jr. and E. W. Cheney, Best approximation problems in tensor-product spaces, Pacific J. Math. 102 (1982), no. 2, 437–446. MR 686562, DOI 10.2140/pjm.1982.102.437
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 279-282
- MSC: Primary 41A65; Secondary 41A44, 41A50
- DOI: https://doi.org/10.1090/S0002-9939-1982-0667289-4
- MathSciNet review: 667289