Geodesic
Optimal Constants in Khintchine Type Inequalities for Fermions, Rademachers and $q$-Gaussian Operators
Artur Buchholz1
1 Institute of Mathematics University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wroc/law, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 3, pp. 315-321

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For $(P_{k})$ being Rademacher, Fermion or $q$-Gaussian ($-1\leq q\leq0$) operators, we find the optimal constants $C_{2n}$, $n\in\Bbb N$, in the inequality $$ \Big\| \sum_{k=1}^N A_k \otimes P_k \Big\|_{2n} \leq [C_{2n}]^{1/2n} \max \Big\{ \Big\| \Big( \sum_{k=1}^N A_k^* A_k \Big)^{1/2} \Big\|_{L_{2n}}, \Big\| \Big( \sum_{k=1}^N A_k A_k^* \Big)^{1/2} \Big\|_{L_{2n}} \Big\},$$ valid for all finite sequences of operators $(A_{k})$ in the non-commutative $L_{2n}$ space related to a semifinite von Neumann algebra with trace. In particular, $C_{2n}=(2nr-1)!!$ for the Rademacher and Fermion sequences.
DOI : 10.4064/ba53-3-9
Keywords: being rademacher fermion q gaussian leq leq operators optimal constants bbb inequality sum otimes leq max sum * sum a * valid finite sequences operators non commutative space related semifinite von neumann algebra trace particular nr rademacher fermion sequences

Artur Buchholz 1

1 Institute of Mathematics University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wroc/law, Poland 
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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) no. 3, pp. 315-321. doi: 10.4064/ba53-3-9

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