2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124292We prove that if G is a discrete group that admits a metrically proper action on a finite-dimensional CAT(0) cube complex X, then G is weakly amenable. We do this by constructing uniformly bounded Hilbert space representations for which the quantities z^{l(g)} are matrix coefficients. Here l is a length function on G obtained from the combinatorial distance function on the complex X.22 pagesOperator AlgebrasGroup Theory46L99 (Primary) 22D99, 20F65 (Secondary)text