Real Interpolation between Row and Column Spaces

• Autorzy: Pisier G.

Identyfikatory

DOI

10.4064/ba59-3-6

• Języki publikacji: EN

Abstrakty

EN

We give an equivalent expression for the K-functional associated to the pair of operator spaces (R,C) formed by the rows and columns respectively. This yields a description of the real interpolation spaces for the pair (M_n(R),M_n(C)) (uniformly over n). More generally, the same result is valid when M_n (or B(ℓ₂)) is replaced by any semi-finite von Neumann algebra. We prove a version of the non-commutative Khintchine inequalities (originally due to Lust-Piquard) that is valid for the Lorentz spaces L_p,q(τ) associated to a non-commutative measure τ, simultaneously for the whole range 1≤p,q<∞, regardless of whether p<2 or p>2. Actually, the main novelty is the case p=2, q/=2. We also prove a certain simultaneous decomposition property for the operator norm and the Hilbert–Schmidt norm.

Słowa kluczowe

EN

real interpolation method; row and column operator space; K-functional; non-commutative Khintchine inequality; non-commutative Lorentz space

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: Vol. 59, no 3
• Strony: 237--259
• Opis fizyczny: Bibliogr. 30 poz.

Twórcy

autor

Pisier G.

• Mathematics DepartmentTexas A&M University College Station, TX 77843, U.S.A
• Université Paris VI Institut Mathématique de Jussieu Analyse Fonctionnelle, Case 186 75252 Paris Cedex 05, France

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