Numerical ranges and compressions of Sn-matrices

Hwa Long Gau, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Let A be an n-by-n (n ≥ 2) Sn -matrix, that is, A is a contraction with eigenvalues in the open unit disc and with rank (In - A*A) = 1, and let W(A) denote its numerical range. We show that (1) if B is a k-by-k (1 ≤ k < n) compression of A, then W(B) ⊂≠ W(A), (2) if A is in the standard upper-triangular form and B is a k-by-k (1 ≤ k < n) principal submatrix of A, then ∂W(B) ∩ ∂W(A) = ∅, and (3) the maximum value of k for which there is a k-by-k compression of A with all its diagonal entries in ∂W(A) is equal to 2 if n = 2, and [n/2] if n≥3.

Original languageEnglish
Pages (from-to)465-476
Number of pages12
JournalOperators and Matrices
Volume7
Issue number2
DOIs
StatePublished - 2013

Keywords

  • Compression
  • Numerical range
  • S-matrix
  • Unitary dilation

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