Isometric Dilations of Commuting Contractions and Brehmer Positivity
Complex Analysis and Operator Theory(2022)
摘要
It is well-known that an n-tuple
$$(n\ge 3)$$
of commuting contractions does not posses an isometric dilation, in general. Considering a class of n-tuple of commuting contractions satisfying certain positivity assumption, we construct their isometric dilations and consequently establish their von Neumann inequality. The positivity assumption is related to Brehmer positivity and motivated by the study of isometric dilations of operator tuples in Barik et al. (Trans Amer Math Soc 372(2):1429–1450, 2019).
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关键词
Brehmer positivity,Isometric dilations,Regular dilations,Hardy space,Von Neumann inequality,47A20,47A13,47A56,47B38,46E22,47B32,32A70
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