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Kittaneh, Fuad; Moslehian, Mohammad Sal; Sababheh, Mohammad
Linear algebra and its applications, 01/2017, Letnik: 513Journal Article
In this paper, motivated by perturbation theory of operators, we present some upper bounds for ⦀f(A)Xg(B)+X⦀ in terms of ⦀|AXB|+|X|⦀ and ⦀f(A)Xg(B)−X⦀ in terms of ⦀|AX|+|XB|⦀, where A,B are G1 operators, ⦀⋅⦀ is a unitarily invariant norm and f,g are certain analytic functions. Further, we find some new upper bounds for the Schatten 2-norm of f(A)X±Xg(B). Several special cases are discussed as well.
