The refined BMV upper bound fails for 3x3 PSD matrices, explained via non-canonical common parts, and a pinching refinement is proposed and proved for the n,2 case as a sandwich inequality.
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On the Failure of the Upper Bound in the Refined BMV Conjecture and a Pinching Correction
The refined BMV upper bound fails for 3x3 PSD matrices, explained via non-canonical common parts, and a pinching refinement is proposed and proved for the n,2 case as a sandwich inequality.