Higher-rank numerical ranges and dilations

Hwa Long Gau; Chi Kwong Li; Pei Yuan Wu

Higher-rank numerical ranges and dilations

Hwa Long Gau, Chi Kwong Li, Pei Yuan Wu

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

16 引文斯高帕斯（Scopus）

摘要

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

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

引用此

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AU - Li, Chi Kwong

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N2 - 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.

AB - 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.

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KW - Unitary dilation

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M3 - 期刊論文

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VL - 63

SP - 181

EP - 189

JO - Journal of Operator Theory

JF - Journal of Operator Theory

IS - 1

ER -

Higher-rank numerical ranges and dilations

摘要

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