Higher-rank Numerical Ranges and Dilations
نویسنده
چکیده
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 Snmatrices.
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