Sets with fixed point property for isometric mappings
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- by Anthony To Ming Lau PDF
- Proc. Amer. Math. Soc. 79 (1980), 388-392 Request permission
Abstract:
A subset K of a Banach space E is said to have the fixed point property for isometric mappings (f. p. p.) if there exists z in K such that $U(z) = z$ for each isometric mapping U from K onto K. We prove that any bounded closed subsets of E with uniform relative normal structure have the f. p. p. We also prove that if E is either $\mathcal {B}(H)$ (bounded operators on a Hilbert space H) or ${l_\infty }(X)$ (bounded functions on X), then E is finite dimensional if and only if each $\mathrm {weak}^*$-compact convex subset of E has the f. p. p. This is also equivalent to the convex set of (normal) states on E having the f. p. p.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 388-392
- MSC: Primary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-1980-0567978-4
- MathSciNet review: 567978