Numerical range of S(φ)

Hwa Long Gau, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

57 Scopus citations

Abstract

We make a detailed study of the numerical ranges W(T) of completely nonunitary contractions T with the property rank (1-T*T)=1 on a finite-dimensional Hilbert space. We show that such operators are completely characterized by the Poncelet property of their numerical ranges, namely, an n-dimensional contraction T is in the above class if and only if for any point λ on the unit circle there is an (n+1)-gon which is inscribed in the unit circle, circumscribed about W(T) and has λ as a vertex. We also obtain a dual form of this property and the information on the inradii of numerical ranges of arbitrary finite-dimensional operators.

Original languageEnglish
Pages (from-to)49-73
Number of pages25
JournalLinear and Multilinear Algebra
Volume45
Issue number1
DOIs
StatePublished - 1998

Keywords

  • Compression of the shift
  • Inradius
  • Jordan block
  • Numerical radius
  • Numerical range
  • Poncelet property

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