Numerical ranges of kms matrices

Hwa Long Gau, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

Abstract

We prove the following properties of the numerical range of a KMS matrix Jn(a): (1) W(Jn(a)) is a circular disc if and only if n = 2 and a ≠ 0, (2) its boundary ?W(Jn(a)) contains a line segment if and only if n ≥ 3 and |a| = 1, and (3) the intersection of the boundaries ?W(Jn(a)) and ∂W(Jn(a)[j]) is either the singleton {min s(Re Jn(a))} if n is odd, j = (n + 1)/2 and |a| > 1, or the empty set Ø if otherwise, where, for any n-by-n matrix A, A[j] denotes its jth principal submatrix obtained by deleting its jth row and jth column (1 ≤ j ≤ n), ReA its real part (A + A*)/2, and s(A) its spectrum.

Original languageEnglish
Pages (from-to)583-610
Number of pages28
JournalActa Scientiarum Mathematicarum
Volume79
Issue number3-4
StatePublished - 2013

Keywords

  • KMS matrix
  • Numerical range
  • S-matrix
  • S -matrix

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