Contractive upper triangular matrices with prescribed diagonals and superdiagonals

2025/06/18 by Renard, Axel
#15A60 #15A83 #30H05 #30H10 #47A08 #47A30 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2506.15444

Abstract

A characterization of the matrix representation of the compressed shift acting on a finite-dimensional model space endowed with the Takenaka-Malmquist-Walsh basis, among all upper triangular matrices, is proved. For a fixed dimension, this matrix is the unique matrix with spectral norm no greater than one and with a prescribed diagonal and superdiagonal. We also discuss an extension to the setting of infinite matrices.

Citations

• Schwarz-Pick type inequalities from an operator theoretical point of view
• Model spaces: a survey

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