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arXiv · 2005.07556

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

Meric Augat·Michael T. Jury·James Eldred Pascoe
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Abstract

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.

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Meric Augat, Michael T. Jury, James Eldred Pascoe. 2020-05-15. Effective noncommutative Nevanlinna-Pick interpolation in the row ball, and applications. https://arxiv.org/abs/2005.07556

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