Optimal inverses and abstract splines

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• 作者：Gustavo Corach^a ; ^b ; ¹ ; ^{gcorach@fi.uba.ar" class="auth_mail" title="E-mail the corresponding author} ; Guillermina Fongi^b ; ¹ ; ^{gfongi@conicet.gov.ar" class="auth_mail" title="E-mail the corresponding author} ; Alejandra Maestripieri^a ; ^b ; ¹ ; ^{amaestri@fi.uba.ar" class="auth_mail" title="E-mail the corresponding author}
• 关键词：41A65 ; 46C05 ; 47A05
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：496
• 期：Complete
• 页码：182-192
• 全文大小：296 K

文摘

We extend the notion of optimal inverse introduced by S.K. Mitra for matrices, to operators in Hilbert spaces. We obtain necessary and sufficient conditions for the existence of these inverses for a closed range operator and apply these results to characterize the solutions of abstract smoothing spline problems.