A characterization of Hilbert space
Author:
Ronald E. Bruck
Journal:
Proc. Amer. Math. Soc. 43 (1974), 173-175
MSC:
Primary 46C05
DOI:
https://doi.org/10.1090/S0002-9939-1974-0341038-7
MathSciNet review:
0341038
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: A real Banach space 
of dimension 
is an inner product space iff there exists a bounded smooth convex subset of 
which is the range of a nonexpansive retraction.
- [1] Errett Bishop and R. R. Phelps, The support functionals of a convex set, Proc. Sympos. Pure Math., Vol. VII, Amer. Math. Soc., Providence, R.I., 1963, pp. 27–35. MR 0154092
- [2] Ronald E. Bruck Jr., Nonexpansive projections on subsets of Banach spaces, Pacific J. Math. 47 (1973), 341–355. MR 0341223
- [3] D. G. de Figueiredo and L. A. Karlovitz, On the extension of contractions on normed spaces, Nonlinear Functional Analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 1, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 95–104. MR 0275120
- [4] S. Kakutani, Some characterizations of Euclidean space, Jap. J. Math. 16 (1939), 93–97. MR 0000895
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46C05
Retrieve articles in all journals with MSC: 46C05
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1974-0341038-7
Keywords:
Nonexpansive retract
Article copyright:
© Copyright 1974
American Mathematical Society
