Every definite continuous inner product on the Hilbert-Schmidt operator space admits a representation with one unavoidable negative term, with an all-positive form under an additional dominance condition.
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Inner products on the Hilbert space $S_2$ of Hilbert--Schmidt operators
Every definite continuous inner product on the Hilbert-Schmidt operator space admits a representation with one unavoidable negative term, with an all-positive form under an additional dominance condition.