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dc.contributor.authorGau, Hwa-Longen_US
dc.contributor.authorWang, Kuo-Zhongen_US
dc.date.accessioned2020-10-05T02:01:02Z-
dc.date.available2020-10-05T02:01:02Z-
dc.date.issued2020-10-01en_US
dc.identifier.issn0024-3795en_US
dc.identifier.urihttp://dx.doi.org/10.1016/j.laa.2020.05.039en_US
dc.identifier.urihttp://hdl.handle.net/11536/155089-
dc.description.abstractLet K-2 = [GRAPHICS}, K-n be the n x n weighted shift matrix with weights root 2, [GRAPHICS}, root 2 for all n >= 3, and K-infinity be the weighted shift operator with weights root 2, 1, 1, 1, .... In this paper, we show that if an n x n nonzero matrix A satisfies W(A(k)) = W(A) for all 1 <= k <= n, then W(A) cannot be a (nondegenerate) circular disc. Moreover, we also show that W(A) = W(A(n-1)) = {z is an element of C : vertical bar z vertical bar <= 1} if and only if A is unitarily similar to K-n. Finally, we prove that if T is a numerical contraction on an infinite-dimensional Hilbert space H, then lim(n ->infinity) parallel to T(n)x parallel to = root 2 for some unit vector x is an element of H if and only if T is unitarily similar to an operator of the form K-infinity circle plus T' with w(T') <= 1. (C) 2020 Elsevier Inc. All rights reserved.en_US
dc.language.isoen_USen_US
dc.subjectNumerical rangeen_US
dc.subjectNumerical radiusen_US
dc.subjectNumerical contractionen_US
dc.titleMatrix powers with circular numerical rangeen_US
dc.typeArticleen_US
dc.identifier.doi10.1016/j.laa.2020.05.039en_US
dc.identifier.journalLINEAR ALGEBRA AND ITS APPLICATIONSen_US
dc.citation.volume603en_US
dc.citation.spage190en_US
dc.citation.epage211en_US
dc.contributor.department應用數學系zh_TW
dc.contributor.departmentDepartment of Applied Mathematicsen_US
dc.identifier.wosnumberWOS:000556369500012en_US
dc.citation.woscount0en_US
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