Rank two perturbations of matrices and operators and operator model for t-transformation of probability measures

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• 作者：Anna Kula^a ; ¹ ; ^{anna.kula@math.uni.wroc.pl} ; Michał Wojtylak^b ; ² ; ^{michal.wojtylak@im.uj.edu.pl} ; Janusz Wysoczański^a ; ³ ; ^{janusz.wysoczanski@math.uni.wroc.pl}
• 关键词：47A55 ; 15A18 ; 46C20 ; 46L53 ; 46N30
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：272
• 期：3
• 页码：1147-1181
• 全文大小：702 K
• 卷排序：272

文摘

Rank two parametric perturbations of operators and matrices are studied in various settings. In the finite dimensional case the formula for a characteristic polynomial is derived and the large parameter asymptotics of the spectrum is computed. The large parameter asymptotics of a rank one perturbation of singular values and condition number are discussed as well. In the operator case the formula for a rank two transformation of the spectral measure is derived and it appears to be the t-transformation of a probability measure, studied previously in the free probability context. New transformation of measures is studied and several examples are presented.