On some perturbation inequalities for operators

Bhatia, Rajendra ; Kittaneh, Fuad (1988) On some perturbation inequalities for operators Linear Algebra and its Applications, 106 . pp. 271-279. ISSN 0024-3795

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/002437...

Related URL: http://dx.doi.org/10.1016/0024-3795(88)90034-1


An estimate for the norm of the solution to the equation AX-XB=S obtained by R. Bhatia, C. Davis, and A. McIntosh for normal operators A and B is shown to be valid for a larger class. Some other inequalities in the same spirit are obtained, including a "sin θ theorem" for singular vectors. Some inequalities concerning the continuity of the map A→|itA| obtained recently by Kittaneh and Kosaki are extended using these ideas.

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