Norm inequalities for sums and differences of positive operators
type: Item
instance of: scholarly article
title: Norm inequalities for sums and differences of positive operators
zbMATH Open document ID: 1063.47005
author: Fuad Kittaneh
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
review text: The author gives the following inequality: For positive operators \(A\) and \(B\), \[ \begin{multlined} 2| A\oplus B \oplus 0\oplus 0 | \leq | (A-B)\oplus (A-B)\oplus 0\oplus 0 | + | A\oplus A\oplus B\oplus B| \\ + | A^{\frac{1}{2}} B^{\frac{1}{2}}\oplus A^{\frac{1}{2}} B^{\frac{1}{2}} \oplus A^{\frac{1}{2}} B^{\frac{1}{2}}\oplus A^{\frac{1}{2}}B^{\frac{1}{2}} | ,\end{multlined} \] where \(| \cdot | \) means any unitarily invariant norm. Especially, in the usual operator norm case, it becomes the following inequality: \[ \max(\| A\| , \| B\| )-\| A^{\frac{1}{2}}B^{\frac{1}{2}}\| \leq \| A-B\| . \] Moreover, the author gives some comments on some norm inequalities related to the sum and difference of \(A\) and \(B\).
reviewed by: Takeaki Yamazaki
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47B15
zbMATH DE Number: 2081923
zbMATH Keywords: operator matrix
zbMATH Keywords: positive operator
zbMATH Keywords: unitarily invariant norm
zbMATH Keywords: norm inequality
MaRDI profile type: Publication
full work available at URL: j.laa.2003.11.023
OpenAlex ID: W2049710258
cites work: On the Singular Values of a Product of Operators
cites work: Norm inequalities for positive operators
cites work: CLARKSON INEQUALITIES WITH SEVERAL OPERATORS
cites work: Q3701974
cites work: Norm estimates related to self-commutators
cites work: NORM INEQUALITIES EQUIVALENT TO LÖWNER-HEINZ THEOREM
cites work: Interpolation zwischen den Klassen 𝔖p von Operatoren in Hilberträumen
cites work: Non-commutative Clarkson inequalities for unitarily invariant norms.
cites work: Norm inequalities for certain operator sums
cites work: Commutator inequalities associated with the polar decomposition
cites work: Q4422017
cites work: Q3857325
cites work: Matrix inequalities
cites work: On some matrix inequalities.
DOI: 10.1016/J.LAA.2003.11.023
description: scientific article; zbMATH DE number 2081923