It is shown that if A is a bounded linear operator on a complex Hilbert space, then 1 4\| A^* A + AA^* \| ≤ ( w(A ) )² ≤ 1 2\| A^* A + AA^* \| , where w(· ) and \| · \| are the numerical radius and the u
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Fuad Kıttaneh (2005) studied this question.
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