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$L_∞$-Khintchine-Bonami inequality in free probability

100%

Buchholz A.

Banach Center Publications

1998

tom 43

nr 1

105-109

We prove the norm estimates for operator-valued functions on free groups supported on the words with fixed length ($f = ∑_{|w| = l} a_{w} ⊗ λ(w)$). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.

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

100%

Buchholz A.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

tom 53

nr 3

315-321

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.

Ograniczanie wyników

1 Banach Center Publications

1 Bulletin of the Polish Academy of Sciences. Mathematics

2 Buchholz A.

1 2005

1 1998

Wyniki wyszukiwania

$L_∞$-Khintchine-Bonami inequality in free probability

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