Journal of Operator Theory
Volume 78, Issue 1, Summer 2017 pp. 3-20.
On ρ-dilations of commuting operatorsAuthors: Vladimir Muller
Author institution: Mathematical Institute, Czech Academy of Sciences, Zitna 25, 115 67 Prague 1, Czech Republic
Summary: Let n⩾ and let c_{F,G} be given real numbers defined for all pairs of disjoint subsets F,G\subset\{1,\dots,n\}. We characterize commuting n-tuples of operators T=(T_1,\dots,T_n) acting on a Hilbert space H which have a commuting unitary dilation U=(U_1,\ldots,U_n)\in B(K)^n, K\supset H such that P_HU^{*\beta}U^\alpha |_H= c_{\supp\alpha,\,\supp\beta} T^{*\beta}T^\alpha for all \alpha,\beta\in\mathbb{Z}_+^n, \supp\,\alpha\cap\supp\,\beta=\emptyset. This unifies and generalizes the concepts of \rho-dilations of a single operator and of regular unitary dilations of commuting n-tuples. We discuss also other interesting cases.
DOI: http://dx.doi.org/10.7900/jot.2016may03.2105
Keywords: \rho-dilation, regular unitary dilation
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