HIGHER-RANK NUMERICAL RANGES AND DILATIONS

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/51133

Title:	HIGHER-RANK NUMERICAL RANGES AND DILATIONS
Authors:	Gau,HL;Li,CK;Wu,PY
Contributors:	數學系
Keywords:	PONCELET CURVES;MATRICES;POLYGONS;UNITARY
Date:	2010
Issue Date:	2012-03-27 18:22:51 (UTC+8)
Publisher:	國立中央大學
Abstract:	For any n-by-n complex matrix A and any k, 1 <= k <= n, let Lambda(k)(A) = {lambda is an element of C : XAX = lambda I(k) for some n-by-k X satisfying XX = I(k)) be its rank-k numerical range. It is shown that if A is an n-by-n contraction, then Lambda(k)(A) = boolean AND{Lambda(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.
Relation:	JOURNAL OF OPERATOR THEORY
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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