On Commuting Families of Nonexpansive Operators
Gideon Schechtman · Proceedings of the American Mathematical Society · 1982
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.