Constrained von Neumann inequalities, higher rank numarical range and applications to harmonic analysis
type: Dataset
description: This thesis joins in the field of operator theory. We are specially interested by the extremal operator S(Φ) defined by the compression of the unilateral shift S to the model subspace H(Φ) where Φ is an inner function on the unit disc. The numerical radius of S(Φ) seems to be important and have many applications to harmonic analysis. C. Badea and G. Cassier showed that there is a relationship between the numerical radius of such operators and the Taylor coefficients of positive rational functions. We give an extension of C. Badea and G. Cassier result and an explicit formula of the numerical radius of S(Φ) in the particular case where Φ is a finite Blaschke product with unique zero. An estimate in the general case is also established. The second part is devoted to the study of the higher rank-k numerical range denoted by Λk(T) which is the set of all complex number λ satisfying PTP = λP for some rank-k orthogonal projection P. This notion was introduced by M.-D. Choi, D. W. Kribs, et K. Zyczkowski motivated by a problem in Physics. We show that if Sn is the n-dimensional shift then its rank-k numerical range is the circular discentered in zero and with a precise radius
identifier: NNT: 2011LYO10247
issued: 2026-05-09T18:23:04.457042
language: fr
modified: 2026-05-09T18:23:04.457046
contact point: Organization
  fn: CCSD
keyword: compression-shift
keyword: higher-rank-numerical-range
keyword: image-numerique-de-rang-superieur
keyword: inegalites-de-von-neumann
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: matrices-de-toeplitz
keyword: numerical-radius
keyword: operator-theory
keyword: poncelet-property
keyword: propriete-de-poncelet
keyword: rayon-numerique
keyword: shift-tronque
keyword: theorie-des-operateurs
keyword: theses
keyword: toeplitz-matrices
keyword: von-neumann-inequalities
landing page: https://theses.hal.science/tel-00672697

Constrained von Neumann inequalities, higher rank numarical range and applications to harmonic analysis
type: Distribution
format: HTML
issued: 2026-05-09T18:23:04.461392
modified: 2026-05-09T18:23:04.441571
access URL: https://theses.hal.science/tel-00672697

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type: Agent