Unitarily invariant norm inequalities for elementary operators involving G₁ operators

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• 作者：Fuad Kittaneh^a ; ^{fkitt@ju.edu.jo" class="auth_mail" title="E-mail the corresponding author} ; Mohammad Sal Moslehian^b ; ^{moslehian@um.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; Mohammad Sababheh^c ; ^{sababheh@psut.edu.jo" class="auth_mail" title="E-mail the corresponding author} ; ^{sababheh@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A60 ; 30E20 ; 47A30 ; 47B10 ; 47B15 ; 47B20
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：513
• 期：Complete
• 页码：84-95
• 全文大小：301 K

文摘

In this paper, motivated by perturbation theory of operators, we present some upper bounds for ⦀f(A)Xg(B)+X⦀$⦀f(A)Xg(B)+X⦀$ in terms of $⦀|AXB|+|X|⦀$ and ⦀f(A)Xg(B)−X⦀$⦀f(A)Xg(B)-X⦀$ in terms of $⦀|AX|+|XB|⦀$, where A,B$A,B$ are G₁$G_1$ operators, ⦀⋅⦀$⦀\cdot ⦀$ is a unitarily invariant norm and f,g$f,g$ are certain analytic functions. Further, we find some new upper bounds for the Schatten 2-norm of f(A)X±Xg(B)$f(A)X\pm Xg(B)$. Several special cases are discussed as well.