Wyniki wyszukiwania

1

Multipliers of the Hardy space H¹ and power bounded operators

100%

Pisier G.

Colloquium Mathematicum

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2001

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tom 88

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nr 1

57-73

EN

We study the space of functions φ: ℕ → ℂ such that there is a Hilbert space H, a power bounded operator T in B(H) and vectors ξ, η in H such that φ(n) = ⟨Tⁿξ,η⟩. This implies that the matrix $(φ(i+j))_{i,j≥0}$ is a Schur multiplier of B(ℓ₂) or equivalently is in the space (ℓ₁ ⊗̌ ℓ₁)*. We show that the converse does not hold, which answers a question raised by Peller [Pe]. Our approach makes use of a new class of Fourier multipliers of H¹ which we call "shift-bounded". We show that there is a φ which is a "completely bounded" multiplier of H¹, or equivalently for which $(φ(i+j))_{i,j≥0}$ is a bounded Schur multiplier of B(ℓ₂), but which is not shift-bounded on H¹. We also give a characterization of "completely shift-bounded" multipliers on H¹.

2

Real Interpolation between Row and Column Spaces

100%

Pisier G.

Bulletin of the Polish Academy of Sciences. Mathematics

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2011

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tom 59

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nr 3

237-259

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 (Mₙ(R),Mₙ(C)) (uniformly over n). More generally, the same result is valid when Mₙ (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.

3

Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach

51%

Maurey B., Pisier G.

Studia Mathematica

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1976

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tom 58

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nr 1

45-90

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Colloquium Mathematicum

1 Studia Mathematica

3 Pisier G.

1 Maurey B.

1 2011

1 2001

1 1976

Multipliers of the Hardy space H¹ and power bounded operators

Real Interpolation between Row and Column Spaces

Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach