Norm inequalities for commutators of self-adjoint operators

作者：Kittaneh Fuad^*

来源：Integral Equations and Operator Theory, 2008, 62(1): 129-135.

DOI：10.1007/s00020-008-1605-6

• commutator
• normal operator
• self-adjoint operator
• positive operator
• unitarily invariant norm
• norm inequality

Let A, B, and X be bounded linear operators on a complex separable Hilbert space. It is shown that if A and B are self- adjoint with a(1) <= A <= a(2) and b(1) <= B <= b2 for some real numbers a(1), a(2), b(1), and b(2), then for every unitarily invariant norm
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<= max(a(2) - b(1), b(2) - a(1))
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If, in addition, X is positive, then
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<= 1/2 (a(2) - a(1))
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These norm inequalities generalize recent related inequalities due to Kittaneh, Bhatia-Kittaneh, and Wang-Du.

• 出版日期2008-9