Operator inequalities extend to Φ-product tensor algebras with the same constants, but defects are governed by transform-domain commutators, with explicit constructions showing Ω(p) separation and no universally optimal transform.
T-product tensors—Part II: Tail bounds for sums of random t-product ten- sors,
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Operator Inequalities in $\Phi$-Product Tensor Algebras: Invariance and Transform Sensitivity
Operator inequalities extend to Φ-product tensor algebras with the same constants, but defects are governed by transform-domain commutators, with explicit constructions showing Ω(p) separation and no universally optimal transform.