For 1<p<∞, ||D||_{ℓ^p→ℓ^p}=1 if and only if Θ(D^*D)=1, where Θ is the maximal average mass of any finite square submatrix.
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Norm of infinite doubly stochastic matrices
For 1<p<∞, ||D||_{ℓ^p→ℓ^p}=1 if and only if Θ(D^*D)=1, where Θ is the maximal average mass of any finite square submatrix.