Numerical ranges and compressions of Sn-matrices

Hwa Long Gau, Pei Yuan Wu

研究成果: 雜誌貢獻期刊論文同行評審

11 引文 斯高帕斯(Scopus)

摘要

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.

原文???core.languages.en_GB???
頁(從 - 到)465-476
頁數12
期刊Operators and Matrices
7
發行號2
DOIs
出版狀態已出版 - 2013

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