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Article Dans Une Revue Confluentes Mathematici Année : 2011

The multiplicative property characterizes ℓp and Lp norms

Résumé

We show that ℓp norms are characterized as the unique norms which are both invariant under coordinate permutation and multiplicative with respect to tensor products. Similarly, the Lp norms are the unique rearrangement-invariant norms on a probability space such that $\|X Y\|=\|X\|\cdot\|Y\|$ for every pair $X,Y$ of independent random variables. Our proof relies on Cramér's large deviation theorem.

Dates et versions

hal-00574787 , version 1 (08-03-2011)

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Guillaume Aubrun, Ion Nechita. The multiplicative property characterizes ℓp and Lp norms. Confluentes Mathematici, 2011, 03 (4), pp.637. ⟨10.1142/S1793744211000485⟩. ⟨hal-00574787⟩
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