New explicit counterexamples demonstrate that Cesàro means of firmly nonexpansive iterates fail to converge strongly, remaining bounded away or oscillating in norm, in infinite-dimensional Hilbert spaces.
Ghosh: The Basel Problem, arXiv manuscript, 2021.https://arxiv.org/abs/2010.03953
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Ces\`aro means of firmly nonexpansive iterates need not converge strongly
New explicit counterexamples demonstrate that Cesàro means of firmly nonexpansive iterates fail to converge strongly, remaining bounded away or oscillating in norm, in infinite-dimensional Hilbert spaces.