On commuting families of nonexpansive operators
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- by Gideon Schechtman PDF
- Proc. Amer. Math. Soc. 84 (1982), 373-376 Request permission
Abstract:
For each $n$, $1 \leqslant n \leqslant \infty$, there exist a weakly compact, convex subset $W$ of ${L_1}$ and a family $\{ {T_i}\} _{i = 1}^n(\{ {T_i}\} _{i = 1}^\infty {\text { in case }}n = \infty )$ of nonexpansive operators of $W$ into $W$ such that there is no common fixed point for the whole family but any (finite) strict subfamily admits a common fixed point.References
- Dale E. Alspach, A fixed point free nonexpansive map, Proc. Amer. Math. Soc. 82 (1981), no. 3, 423–424. MR 612733, DOI 10.1090/S0002-9939-1981-0612733-0 N. Dunford and J. T. Schwartz, Linear operators. I, Interscience, New York, 1958.
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 373-376
- MSC: Primary 47H09; Secondary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-1982-0640234-3
- MathSciNet review: 640234