Abstract
It is shown that if A and B are operators on a separable complex Hilbert space and if |||. ||| is any unitarily invariant norm, then 2 |||A| p + |B| p ||| |A + B| p + |A - B| p ||| ≤ 2 p-1 ||| |A| p + |B| p ||| for 2 ≤ p < ∞, and 2 p-1 ||| |A| p + |B| p ||| ≤ ||| |A + B| p + |A - B| p ||| ≤ 2 ||| |A| p + |B| p ||| for 0 < p < 2. These inequalities are natural generalizations of some of the classical Clarkson inequalities for the Schatten p-norms. Generalizations of these inequalities to larger classes of functions including the power functions are also obtained.
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