Operator-space Grothendieck inequalities for noncommutative \(L_p\)-spaces

DOI10.1215/S0012-7094-06-13135-6zbMath1129.46048arXivmath/0505306MaRDI QIDQ817954

Quanhua Xu

Publication date: 23 March 2006

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0505306

zbMATH Keywords

von Neumann algebraoperator spacesGrothendieck inequality\(L_p\)-spaces

Mathematics Subject Classification ID

Operator spaces and completely bounded maps (46L07) Noncommutative function spaces (46L52)

Related Items (21)

Rosenthal type inequalities for free chaos ⋮ Interactions between Quantum Probability and Operator Space Theory ⋮ Algebraic Davis decomposition and asymmetric Doob inequalities ⋮ Harmonic analysis on quantum tori ⋮ The little Grothendieck theorem and Khintchine inequalities for symmetric spaces of measurable operators ⋮ Multilinear transference of Fourier and Schur multipliers acting on noncommutative -spaces ⋮ Atomic decompositions for noncommutative martingales ⋮ The sharp weighted maximal inequalities for noncommutative martingales ⋮ Grothendieck’s Theorem, past and present ⋮ A reduction method for noncommutative 𝐿_{𝑝}-spaces and applications ⋮ The Effros-Ruan conjecture for bilinear forms on \(C^{*}\)-algebras ⋮ Maurey's factorization theory for operator spaces ⋮ Embedding of \(C_q\) and \(R_q\) into noncommutative \(L_p\)-spaces, \(1 \leq p < q \leq 2\) ⋮ A transference method in quantum probability ⋮ Completely bounded and ideal norms of multiplication operators and Schur multipliers ⋮ Noncommutative Burkholder/Rosenthal inequalities. II: Applications ⋮ 𝑞-Chaos ⋮ Noncommutative maximal inequalities associated with convex functions ⋮ Remarks on the non-commutative Khintchine inequalities for \(0<p<2\) ⋮ On the relation between completely bounded and \((1,{cb})\)-summing maps with applications to quantum XOR games ⋮ Interpolation and the John–Nirenberg inequality on symmetric spaces of noncommutative martingales

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Grothendieck inequality for bilinear forms on \(C^*\)-algebras
• Applications of the complex interpolation method to a von Neumann algebra: non-commutative \(L^ p\)-spaces
• Representations of completely bounded multilinear operators
• Self-duality for the Haagerup tensor product and Hilbert space factorizations
• Notes on non-commutative integration
• Grothendieck's theorem for noncommutative \(C^*\)-algebras, with an appendix on Grothendieck's constants
• On non-semisplit extensions, tensor products and exactness of group \(C^*\)-algebras
• Bounded linear operators between \(C^*\)-algebras
• Free quasi-free states
• Noncommutative Burkholder/Rosenthal inequalities
• Grothendieck's theorem for operator spaces
• A Grothendieck factorization theorem on 2-convex Schatten spaces
• Interpolation of operator spaces
• Rosenthal type inequalities for free chaos
• A Survey of Completely Bounded Operators
• Doobs inequality for non-commutative martingales
• Completely bounded maps into certain Hilbertian operator spaces
• Fubini's Theorem for Ultraproducts of Noncommutative L_p-Spaces
• The operator Hilbert space 𝑂𝐻, complex interpolation and tensor norms

This page was built for publication: Operator-space Grothendieck inequalities for noncommutative \(L_p\)-spaces