Isometric Dilations of Commuting Contractions and Brehmer Positivity

It is well-known that an n-tuple $$(n\ge 3)$$ of commuting contractions does not posses isometric dilation, in general. Considering a class satisfying certain positivity assumption, we construct their dilations and consequently establish von Neumann inequality. The assumption related to Brehmer motivated by the study operator tuples Barik et al. (Trans Amer Math Soc 372(2):1429–1450, 2019).