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

• Autorzy: Artur Buchholz
• Języki publikacji: EN

Abstrakty

EN

For $(P_{k})$ being Rademacher, Fermion or q-Gaussian (-1 ≤ q ≤ 0) operators, we find the optimal constants $C_{2n}$, n∈ ℕ, in the inequality
$∥∑_{k=1}^{N} A_k ⊗ P_k∥_{2n} ≤ [C_{2n}]^{1/2n} max {∥(∑_{k=1}^{N} A*_k A_k}^{1/2}∥_{L_{2n}}, ∥(∑_{k=1}^{N} A_k A*_k}^{1/2}∥_{L_{2n}}}$,
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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: 53
• Numer: 3
• Strony: 315-321

Daty

wydano

2005

Twórcy

autor

Artur Buchholz

• Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/ba53-3-9