Sums of idempotents and logarithmic residues in zero pattern matrix algebras

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• 作者：Harm Bart^a ; ^{bart@ese.eur.nl" class="auth_mail" title="E-mail the corresponding author} ; Torsten Ehrhardt^b ; ^{tehrhard@ucsc.edu" class="auth_mail" title="E-mail the corresponding author} ; Bernd Silbermann^c ; ^{bernd.silbermann@mathematik.tu-chemnitz.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 15A24 ; secondary ; 05C20 ; 47A56
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 June 2016
• 年：2016
• 卷：498
• 期：Complete
• 页码：262-316
• 全文大小：953 K

文摘

A zero pattern algebra is a matrix subalgebra of C^n×n${\mathbb{C}}^{n\times n}$ determined by a pattern of zeros. The issue in this paper is: under what conditions is a matrix in a zero pattern algebra A$\mathcal{A}$ a sum of (rank one) idempotents in A$\mathcal{A}$ or a logarithmic residue in A$\mathcal{A}$? Here logarithmic residues are contour integrals of logarithmic derivatives of analytic A$\mathcal{A}$-valued functions. It turns out that there is a necessary condition involving certain rank/trace requirements. Although these requirements are generally not sufficient, there are several important cases where they are.