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Further Results on the Isometric Embeddability of \(S_q^m\) into \(S_p^n\)
We study Schatten embeddings through circular means of trace powers. In finite dimensions, a decomposition by singular-value vanishing orders shows that every term of order at most two has a nonnegative coefficient. This yields the classification $\ell_q^2(\C)\hookrightarrow\Sp_p^n$ if and only if $
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