An upper bound for the projection constant
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- by D. R. Lewis PDF
- Proc. Amer. Math. Soc. 103 (1988), 1157-1160 Request permission
Abstract:
There is a positive function $\delta (n)$ of exponential order such that, for any normed space $E$ of dimension $n \geq 2$, the projection constant of $E$ satisfies $\lambda (E) \leq {n^{1/2}}[1 - \delta (n)]$.References
- T. Figiel, J. Lindenstrauss, and V. D. Milman, The dimension of almost spherical sections of convex bodies, Acta Math. 139 (1977), no. 1-2, 53–94. MR 445274, DOI 10.1007/BF02392234
- M. Ĭ. Kadec′ and M. G. Snobar, Certain functionals on the Minkowski compactum, Mat. Zametki 10 (1971), 453–457 (Russian). MR 291770
- Hermann König, Spaces with large projection constants, Israel J. Math. 50 (1985), no. 3, 181–188. MR 793850, DOI 10.1007/BF02761398
- H. König and D. R. Lewis, A strict inequality for projection constants, J. Funct. Anal. 74 (1987), no. 2, 328–332. MR 904822, DOI 10.1016/0022-1236(87)90028-0
- D. R. Lewis, Finite dimensional subspaces of $L_{p}$, Studia Math. 63 (1978), no. 2, 207–212. MR 511305, DOI 10.4064/sm-63-2-207-212
- Albrecht Pietsch, Operator ideals, North-Holland Mathematical Library, vol. 20, North-Holland Publishing Co., Amsterdam-New York, 1980. Translated from German by the author. MR 582655
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 1157-1160
- MSC: Primary 46B25; Secondary 47A30, 47B10
- DOI: https://doi.org/10.1090/S0002-9939-1988-0954999-X
- MathSciNet review: 954999