Unitary part of a contraction

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/51164

Title:	Unitary part of a contraction
Authors:	Gau,HL;Wu,PY
Contributors:	數學系
Date:	2010
Issue Date:	2012-03-27 18:23:42 (UTC+8)
Publisher:	國立中央大學
Abstract:	For a contraction A on a Hilbert space H, we define the index j(A) (resp.. k(A)) as the smallest nonnegative integer j (resp., k) such that ker(I - A(j)A(j)) (resp., ker(I - A(k)A(k)) boolean AND ker(I - A(k)A(k))) equals the subspace of H on which the unitary part of A acts. We show that if n = dim H < infinity, then j(A) <= n (resp., k(A) <= left particularn/2left particular). and the equality holds if and only if A is of class S, (resp., one of the three conditions is true: (1) A is of class S, (2) n is even and A is completely nonunitary with parallel to A(n-2)parallel to = 1 and parallel to A(n-1)parallel to < 1. and (3) n is even and A = U circle times A', where U is unitary on a one-dimensional space and A' is of class S(n-1)). (C) 2010 Elsevier Inc. All rights reserved.
Relation:	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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