2023/10/11 by Bojan Kuzma, Mitja Mastnak, Kuzma, Bojan +5
Mathematics · #15A30 #20G99 #47D03 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2310.07466
openalex publication_date 2023/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notions of ε-approximate fixed point and weak ε-approximate fixed point. We show that for a group of unitary matrices even the existence of a nontrivial weak ε-approximate fixed point for sufficiently small ε gives an actual nontrivial common eigenvector. We give estimates for ε in terms of the size n of matrices and prove that the dependence is polynomial. Moreover, we show that the common eigenvector is polynomially close to the starting weak approximate fixed point.