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Commutant Lifting for Commuting Row Contractions

Abstract

If T=[T1...Tn]T= \big[ T_1 ... T_n\big] is a row contraction with commuting entries, and the Arveson dilation is T~=[T~1...T~n]\tilde T= \big[ \tilde T_1 ... \tilde T_n\big], then any operator XX commuting with each TiT_i dilates to an operator ZZ of the same norm which commutes with each T~i\tilde T_i.Comment: one section and references were adde

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    Last time updated on 03/12/2019