Optimal Constants in Khintchine Type Inequalities for Fermions, Rademachers and q-Gaussian Operators

Artur Buchholz

Artur Buchholz

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005), p. 315-321 / Harvested from The Polish Digital Mathematics Library

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Résumé

For $(P_{k})$ being Rademacher, Fermion or q-Gaussian (-1 ≤ q ≤ 0) operators, we find the optimal constants $C_{2 n}$ , n∈ ℕ, in the inequality $∥ \sum_{k = 1}^{N} A_{k} \otimes P_{k} ∥_{2 n} \leq {[C_{2 n}]}^{1 / 2 n} m a x {∥ (\sum_{k = 1}^{N} A *_{k} A_{k}}^{1 / 2} ∥_{L_{2 n}}, ∥ (\sum_{k = 1}^{N} A_{k} A *_{k}$ 1/2∥L2n $,$ valid for all finite sequences of operators $(A_{k})$ in the non-commutative $L_{2 n}$ space related to a semifinite von Neumann algebra with trace. In particular, $C_{2 n} = (2 n r - 1)!!$ for the Rademacher and Fermion sequences.

Publié le : 2005-01-01

Zbl 1117.46043

EUDML-ID : urn:eudml:doc:280682

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Artur Buchholz. Optimal Constants in Khintchine Type Inequalities for Fermions, Rademachers and q-Gaussian Operators. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 315-321. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-3-9/