The multiplicative property characterizes p and Lp norms
Confluentes Mathematici, Volume 3 (2011) no. 4, pp. 637-647.

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 ‖XY‖ = ‖X‖ ⋅ ‖Y‖ for every pair X, Y of independent random variables. Our proof combines the tensor power trick and Cramér's large deviation theorem.

Published online:
DOI: 10.1142/S1793744211000485
Guillaume Aubrun 1; Ion Nechita 1

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     title = {The multiplicative property characterizes $\ell _p$ and $L_p$ norms},
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Guillaume Aubrun; Ion Nechita. The multiplicative property characterizes $\ell _p$ and $L_p$ norms. Confluentes Mathematici, Volume 3 (2011) no. 4, pp. 637-647. doi : 10.1142/S1793744211000485.

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