Weak* fixed point property of Fourier-Stieltjes algebra on compact groups
DOI:
https://doi.org/10.56764/hpu2.jos.2022.1.1.40-45Abstract
Lau and Mah [3] showed that a Fourier-Stieltjes algebra on a separable compact group has the weak* fixed point property, i.e. every nonexpansive mapping on a weak* compact convex subset of has a fixed point. We extend this result by showing that a similar fixed point property holds for norm continuous and asymptotically nonexpansive mappings.
References
.
D. Alspach, A fixed point free nonexpansive map, Proc. Amer. Math. Soc. (1981), 423-424.
R. D. Holmes and A. T.-M. Lau, Asymptotically nonexpansive actions of topological semigroups and fixed points, Bull. London Math. Soc., 3 (1971), 343–347.
A. T.-M. Lau and P. Mah, Fixed point properties for Banach algebras associated to locally compact groups, J. Funct. Anal., 258 (2010), 357–372.
S. Saeidi, F. Golkar and A. M. Forouzanfar, Existence of fixed points for asymptotically nonexpansive type actions of semigroups, J. Fired Point Theory Appl., 20 (2018), no. 2, Art. 72.
J. Schauder, Der Fixpunktsatz in Funktionalraumen, Studia Math., 2 (1930), 171-180.
