標題: | Unitary part of a contraction |
作者: | Gau, Hwa-Long Wu, Pei Yuan 應用數學系 Department of Applied Mathematics |
關鍵字: | Contraction Unitary part;Completely nonunitary part;S(n)-operator;Norm-one index |
公開日期: | 15-六月-2010 |
摘要: | 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. |
URI: | http://dx.doi.org/10.1016/j.jmaa.2010.01.040 http://hdl.handle.net/11536/5266 |
ISSN: | 0022-247X |
DOI: | 10.1016/j.jmaa.2010.01.040 |
期刊: | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS |
Volume: | 366 |
Issue: | 2 |
起始頁: | 700 |
結束頁: | 705 |
顯示於類別: | 期刊論文 |