Comprehensive survey on an order preserving operator inequality
type: Item
instance of: scholarly article
title: Comprehensive survey on an order preserving operator inequality
zbMATH Open document ID: 1276.47020
author: Takayuki Furuta
published in: Banach Journal of Mathematical Analysis
publication date: 2013-03-20T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bjma/1358864546
review text: The paper contains a brief survey on recent results on a certain operator inequality and its applications, namely, \(A \geq B \geq 0 \Longrightarrow (A^{\frac {r}{2}} A^p A^{\frac {r}{2}})^{\frac{1}{q}} \geq (A^{\frac {r}{2}} B^p A^{\frac {r}{2}})^{\frac{1}{q}}\) holds for \(p\geq 0\), \(q\geq 1\), \(r\geq 0\) with \((1+r)q \geq p+r \). This is an extension of the Löwner-Heinz inequality. The author gives a geometrical interpretation of the above inequality.
reviewed by: V. Lokesha
Mathematics Subject Classification ID: 47A63
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 47B20
zbMATH DE Number: 6147117
zbMATH Keywords: Löwner-Heinz inequality
zbMATH Keywords: Furuta inequality
zbMATH Keywords: order preserving operator inequality
zbMATH Keywords: operator monotone function
MaRDI profile type: Publication
OpenAlex ID: W2033538769
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Comprehensive survey on an order preserving operator inequality (DOI)
DOI: 10.15352/BJMA/1358864546