Ando's theorem for nonnegative forms
type: Item
instance of: scholarly article
title: Ando's theorem for nonnegative forms
zbMATH Open document ID: 1284.47001
author: T. Titkos
published in: Positivity
publication date: 2013-01-02T00:00:00Z
review text: A necessary and sufficient condition for the existence of the infimum of two nonnegative forms is obtained as a generalization of Ando's theorem on the problem of the infimum (in the positive cone) of two positive operators acting in a Hilbert space (see [\textit{T. Ando}, Math. Appl., Dordr. 478, 1--12 (1999; Zbl 0995.47044)]). The author makes use of the concepts of parallel sum and Lebesque type decomposition of nonnegative forms [\textit{S. Hassi}, \textit{Z. Sebestyen} and \textit{H. S. V. de Snoo}, J. Funct. Anal. 257, No. 12, 3858--3894 (2009; Zbl 1185.47002)].
Mathematics Subject Classification ID: 47A07
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 47B65
zbMATH DE Number: 6121304
zbMATH Keywords: nonnegative sesquilinear forms
zbMATH Keywords: nonnegative bounded operators
zbMATH Keywords: parallel sum
zbMATH Keywords: generalized short
zbMATH Keywords: Lebesgue type decomposition
zbMATH Keywords: almost dominated part
reviewed by: Edward L. Pekarev
MaRDI profile type: Publication
full work available at URL: s11117-011-0133-9
OpenAlex ID: W2067293769
cites work: Shorted Operators
cites work: Shorted Operators. II
cites work: Series and parallel addition of matrices
cites work: Q4104874
cites work: Problems of infimum in the positive cone
cites work: On operator ranges
cites work: Lebesgue type decompositions for nonnegative forms
cites work: Order Properties of Bounded Self-Adjoint Operators
cites work: Infima of Hilbert space effects
cites work: Functional calculus for sesquilinear forms and the purification map
DOI: 10.1007/S11117-011-0133-9
description: scientific article; zbMATH DE number 6121304