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A Counterexample to Horn's Coincidence Conjecture
Abstract
Horn conjectured that whenever K is a nonempty compact convex subset of a Banach space and F,G:K→ K are continuous commuting maps, there exists x∈ K such that F(x)=G(x). We give a counterexample in a separable Hilbert space. The construction uses an exactly commuting ladder of coincidence-free maps between finite trees, due to Oversteegen and Rogers.
Related
BibTeX
@misc{temur2026counterexample,
title = {{A Counterexample to Horn's Coincidence Conjecture}},
author = {Faruk Temur},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06247},
eprint = {2609.06247},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06247},
}
RIS
TY - UNPB
TI - A Counterexample to Horn's Coincidence Conjecture
AU - Faruk Temur
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.06247
UR - https://arxiv.org/abs/2609.06247
AB - Horn conjectured that whenever K is a nonempty compact convex subset of a Banach space and F,G:K→ K are continuous commuting maps, there exists x∈ K such that F(x)=G(x). We give a counterexample in a separable Hilbert space. The construction uses an exactly commuting ladder of coincidence-free maps between finite trees, due to Oversteegen and Rogers.
ER -