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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:492

Article

Augat, Meric¹  Jury, Michael T.²  Pascoe, James Eldred² 

[1] Washington Univ, St Louis, MO 63110 USA

[2] Univ Florida, Gainesville, FL 32611 USA

关键词: Nevanlinna-Pick interpolation;    Free semigroup algebra;    Noncommutative function theory;   

DOI  :  10.1016/j.jmaa.2020.124457

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free