Some norm inequalities concerning generalized inverses
type: Item
instance of: scholarly article
title: Some norm inequalities concerning generalized inverses
zbMATH Open document ID: 0761.15002
DOI: 10.1016/0024-3795(92)90045-C
published in: Linear Algebra and its Applications
publication date: 1992-10-26T00:00:00Z
review text: The von Neumann-Schatten class \({\mathcal C}_ p\) consists of the compact linear operators \(A\) on a Hilbert space such that the eigenvalues of \((A^*A)^{1/2}\) are in \(\ell^ p\). This paper extends \textit{R. Penrose}'s result on the minimization of \(\| AX-B\|_ 2\) to the \(\|\cdot\|_ p\) norm on \({\mathcal C}_ p\) [Proc. Camb. Philos. Soc. 52, 17-19 (1956; Zbl 0070.125)]. Related minimization problems are also considered.
reviewed by: Stephen L. Campbell
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 47B07
zbMATH DE Number: 69523
zbMATH Keywords: norm inequalities
zbMATH Keywords: generalized inverses
zbMATH Keywords: von Neumann-Schatten class
zbMATH Keywords: compact linear operators
zbMATH Keywords: Hilbert space
zbMATH Keywords: eigenvalues
author: P. J. Maher
MaRDI profile type: Publication
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full work available at URL: 0024-3795(92)90045-c
OpenAlex ID: W4206731440
description: scientific article; zbMATH DE number 69523