 Schatten norm Hölder inequality

ID: schatten-norm-holder-inequality

∥ A B ∥_{r} \leq ∥ A ∥_{p} ∥ B ∥_{q}

when

1/ r = 1/ p + 1/ q

. In particular, the product of two Hilbert-Schmidt operators is trace class and

∥ A B ∥_{1} \leq ∥ A ∥_{HS} ∥ B ∥_{HS} .

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