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arXiv · 0906.4526

Commutant Lifting for Commuting Row Contractions

Kenneth R. Davidson·Trieu Le
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Abstract

If $T= \big[ T_1 ... T_n\big]$ is a row contraction with commuting entries, and the Arveson dilation is $\tilde T= \big[ \tilde T_1 ... \tilde T_n\big]$, then any operator $X$ commuting with each $T_i$ dilates to an operator $Z$ of the same norm which commutes with each $\tilde T_i$.

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Kenneth R. Davidson, Trieu Le. 2009-09-15. Commutant Lifting for Commuting Row Contractions. https://doi.org/10.1112/blms%2Fbdq016

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