Further unitarily invariant norm inequalities for positive semidefinite matrices

In this paper, we prove further unitarily invariant norm inequalities for positive semidefinite matrices. These inequalities generalize earlier related inequalities. Among other applications of our new inequalities, we prove that X Z + Z Y ≤ max X , Y Z + 1 2 X ∗ Z + Z Y ∗ for all n × n complex matr...

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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2022-02, Vol.26 (1), Article 8
Main Authors: Al-Natoor, Ahmad, Kittaneh, Fuad
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Econometrics
Fourier Analysis
Inequalities
Invariants
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Norms
Operator Theory
Potential Theory
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Summary:In this paper, we prove further unitarily invariant norm inequalities for positive semidefinite matrices. These inequalities generalize earlier related inequalities. Among other applications of our new inequalities, we prove that X Z + Z Y ≤ max X , Y Z + 1 2 X ∗ Z + Z Y ∗ for all n × n complex matrices X ,  Y ,  and Z . Here, · denotes the spectral norm.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-022-00876-3