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

Artur Buchholz

Bulletin of the Polish Academy of Sciences. Mathematics (2005)

  • Volume: 53, Issue: 3, page 315-321
  • ISSN: 0239-7269

Abstract

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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 ∥ ∑ k = 1 N A k ⊗ P k ∥ 2 n ≤ [ C 2 n ] 1 / 2 n m a x ∥ ( ∑ k = 1 N A * k A k 1 / 2 ∥ L 2 n , ∥ ( ∑ 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.

How to cite

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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 53.3 (2005): 315-321. <http://eudml.org/doc/280682>.

@article{ArturBuchholz2005,
abstract = {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$1/2∥L2n$, $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. },
author = {Artur Buchholz},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Khintchine inequality; non-commutative analysis; commutation relations; Rademacher functions},
language = {eng},
number = {3},
pages = {315-321},
title = {Optimal Constants in Khintchine Type Inequalities for Fermions, Rademachers and q-Gaussian Operators},
url = {http://eudml.org/doc/280682},
volume = {53},
year = {2005},
}

TY - JOUR
AU - Artur Buchholz
TI - Optimal Constants in Khintchine Type Inequalities for Fermions, Rademachers and q-Gaussian Operators
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2005
VL - 53
IS - 3
SP - 315
EP - 321
AB - 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$1/2∥L2n$, $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.
LA - eng
KW - Khintchine inequality; non-commutative analysis; commutation relations; Rademacher functions
UR - http://eudml.org/doc/280682
ER -

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