Commutant Lifting for Commuting Row Contractions

Abstract

If $T=[T_1...T_n]$ is a row contraction with commuting entries, and the Arveson dilation is $\tilde{T}=[{\tilde{T}}_1...{\tilde{T}}_n]$, then any operator $X$ commuting with each $T_i$ dilates to an operator $Z$ of the same norm which commutes with each ${\tilde{T}}_i$.

one section and references were added

Cited by in corpus (5)

• Factorization in weak products of complete Pick spaces
• Commutant lifting in several variables
• Connecting Commuting Normal Matrices
• Isometric dilation and Sarason's commutant lifting theorem in several variables
• Commutant lifting and Nevanlinna-Pick interpolation in several variables