Higher-rank numerical ranges and dilations

Hwa Long Gau, Chi Kwong Li, Pei Yuan Wu

研究成果: 雜誌貢獻期刊論文同行評審

13 引文 斯高帕斯(Scopus)

摘要

For any n-by-n complex matrix A and any k, 1 ≤ k ≤ n, let Λk(A) = {λ ∈ C: X*AX = λIk for some n-by-k X satisfying X*X = Ik} be its rank-k numerical range. It is shown that if A is an n-by-n contraction, then Λk(A) = {Λk(U): U is an (n + dA)-by-(n + dA) unitary dilation of A}, where dA = rank (In - A*A). This extends and refines previous results of Choi and Li on constrained unitary dilations, and a result of Mirman on Sn- matrices.

原文???core.languages.en_GB???
頁(從 - 到)181-189
頁數9
期刊Journal of Operator Theory
63
發行號1
出版狀態已出版 - 12月 2010

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