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Some results on the radial projection in Banach spaces


Author: R. L. Thele
Journal: Proc. Amer. Math. Soc. 42 (1974), 483-486
MSC: Primary 46B05
DOI: https://doi.org/10.1090/S0002-9939-1974-0328550-1
MathSciNet review: 0328550
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Abstract: We obtain in this paper some new theorems on the radial projection onto the unit ball in Banach spaces, including in particular the following: A Banach space X is uniformly nonsquare if and only if the radial projection in X has Lipschitz constant strictly less than 2.


References [Enhancements On Off] (What's this?)

  • [1] D. G. deFigueiredo and L. A. Karlovitz, On the radial projection in normed spaces, Bull. Amer. Math. Soc. 73 (1967), 364-368. MR 35 #2130. MR 0211248 (35:2130)
  • [2] C. F. Dunkl and K. S. Williams, A simple norm inequality, Amer. Math. Monthly 71 (1964), 53-54. MR 1532478
  • [3] K. Goebel, Convexity of balls and fixed-point theorems for mappings with non-expansive square, Compositio Math. 22 (1970), 269-274. MR 42 #8355. MR 0273477 (42:8355)
  • [4] R. C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc. 61 (1947), 265-292. MR 9, 42. MR 0021241 (9:42c)
  • [5] -, Uniformly non-square Banach spaces, Ann. of Math. (2) 80 (1964), 542-550. MR 30 #4139. MR 0173932 (30:4139)
  • [6] W. A. Kirk and M. F. Smiley, Another characterization of inner product, Amer. Math. Monthly 71 (1964), 890-891. MR 1532903

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DOI: https://doi.org/10.1090/S0002-9939-1974-0328550-1
Article copyright: © Copyright 1974 American Mathematical Society

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