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Paper detail

Effective noncommutative Nevanlinna-Pick interpolation in the row ball, and applications

We provide an effective single-matrix criterion, in terms of what we call the elementary Pick matrix, for the solvability of the noncommutative Nevanlinna-Pick interpolation problem in the row ball, and provide some applications. In particular we show that the so-called "column-row property" fails for the free semigroup algebras, in stark contrast to the analogous commutative case. Additional applications of the elementary Pick matrix include a local dilation theorem for matrix row contractions and interpolating sequences in the noncommutative setting. Finally we present some numerical results related to the failure of the column-row property.

preprint2020arXivOpen access
Meric AugatMichael T. JuryJames Eldred Pascoe
math.FA
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Meric AugatMichael T. JuryJames Eldred Pascoe

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