The representation and approximation for the weighted Moore-Penrose inverse in Hilbert space.
type: Item
instance of: scholarly article
title: The representation and approximation for the weighted Moore-Penrose inverse in Hilbert space.
zbMATH Open document ID: 1038.47002
DOI: 10.1016/S0096-3003(02)00071-1
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: Let \(X\), \(Y\) be Hilbert spaces and let \(T: X\to Y\) be a bounded linear operator with closed range. Let \(M: Y\to Y\) and \(N:X\to X\) be positive definite linear operators. Then \(T^+_{MN}\) is said to be the weighted Moore-Penrose inverse of \(T\) if it is the unique linear operator satisfying \(TT^+_{MN}T= T\), \(T^+_{MN} TT^+_{MN}= T^+_{MN}\), \((MTT^+_N)^*= MTT^+_{MN}\), \((NT^+_{MN})^*= NT^*_{MN}T\). When \(X= \mathbb{C}^n\), \(Y= \mathbb{C}^m\), \(M= I_m\), \(N= I_n\), the weighted Moore-Penrose inverse is reduced to the Moore-Penrose inverse \(T^+\). In the paper under review, the author presents a representation and an approximation for the weighted Moore-Penrose inverses in Hilbert spaces.
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 65J10
zbMATH DE Number: 1861403
zbMATH Keywords: weighted Moore-Penrose inverse
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: representation
zbMATH Keywords: approximation
zbMATH Keywords: Hilbert space
zbMATH Keywords: closed range
zbMATH Keywords: bounded operator
author: Yimin Wei
reviewed by: Danuta Przeworska-Rolewicz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1861403