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dc.contributor.author吳培元en_US
dc.contributor.authorWU PEI YUANen_US
dc.date.accessioned2014-12-13T10:47:36Z-
dc.date.available2014-12-13T10:47:36Z-
dc.date.issued2009en_US
dc.identifier.govdocNSC96-2115-M009-013-MY3zh_TW
dc.identifier.urihttp://hdl.handle.net/11536/101084-
dc.identifier.urihttps://www.grb.gov.tw/search/planDetail?id=1749462&docId=298076en_US
dc.description.abstract在此一三年期的研究計畫中,我們將對在希伯特空間上的有界線性算子的數值域 作一有系統而詳盡的研究。第一年中,我們將集中心力於有限維空間上的算子或有限 矩陣。基於過去所作的相關研究成果,我們將專注於兩類矩陣,即Sn -矩陣和伴隨矩陣。 第二年將考慮其他類型的矩陣,例如Toeplitz 矩陣、Hankel 矩陣和形如, 1 [ ]n ij i j a = 之矩陣, 其中對每一k (1 ? k ? n),i=k或j=k時, ij a 之值均相同。我們希望對比此等矩陣之數 值域和其無窮維空間上的對應算子二者性質之共同與相異之處。第三年將專注於無窮 維空間上算子數值域之研究。我們特別想解決一已懸疑多年的問題:設A 為二次型算 子且B和A可交換,則是否w(AB) ? A w(B)和w(AB) ? w(A) B 成立,此處w(?)表示 算子之數值半徑。zh_TW
dc.description.abstractIn this three-year project, we plan to launch a detailed study of properties of the numerical ranges of bounded linear operators on a complex Hilbert space. For the first year, we will concentrate on operators on finite-dimensional spaces, which amount to the same as finite matrices. Based on our previous works, we will concentrate on two types of matrices, namely, the n S -matrices and companion matrices. In the second year, we move onto other types of finite matrices such as the Toeplitz matrices, Hankel matrices and matrices of the form , 1 [ ]n ij a i j= with the aij 刪s identical for i=k or j=k (1 . k . n) . Properties of their numerical ranges will be contrasted with the ones for their infinite-dimensional analogues. The third year will be devoted to the study of numerical ranges of infinite-dimensional operators. We have in mind in particular of proving the numerical radius inequalities w(AB) . A w(B) and w(AB) . w(A) B for a quadratic operator A commuting with an operator B .en_US
dc.description.sponsorship行政院國家科學委員會zh_TW
dc.language.isozh_TWen_US
dc.subject數值域zh_TW
dc.subjectn S -矩陣zh_TW
dc.subject伴隨矩陣zh_TW
dc.subjectToeplitz 矩陣zh_TW
dc.subjectHankel 矩陣zh_TW
dc.subject數值半徑zh_TW
dc.subjectNumerical rangeen_US
dc.subjectn S -matrixen_US
dc.subjectcompanion matrixen_US
dc.subjectToeplitz matrixen_US
dc.subjectHankel matrixen_US
dc.subjectnumerical radius.en_US
dc.title有界算子數值域的研究zh_TW
dc.titleNumerical Ranges of Bounded Operatorsen_US
dc.typePlanen_US
dc.contributor.department國立交通大學應用數學系(所)zh_TW
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