منابع مشابه
HOMOGENEOUS HILBERTIAN SUBSPACES OF NON-COMMUTATIVE Lp SPACES
December 22, 1999 Abstract. Suppose A is a hyperfinite von Neumann algebra with a normal faithful normalized trace τ . We prove that if E is a homogeneous Hilbertian subspace of Lp(τ) (1 ≤ p < ∞) such that the norms induced on E by Lp(τ) and L2(τ) are equivalent, then E is completely isomorphic to the subspace of Lp([0, 1]) spanned by Rademacher functions. Consequently, any homogeneous Hilberti...
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We prove the following noncommutative version of Lewis’s classical result. Every n-dimensional subspace E of Lp(M) (1 < p < ∞) for a von Neumann algebra M satisfies dcb(E,RC n p ) ≤ cp · n ̨̨ ̨ 1 2 − 1 p ̨̨ ̨ for some constant cp depending only on p, where 1 p + 1 p = 1 and RC p = [Rn∩ Cn, Rn +Cn] 1 p . Moreover, there is a projection P : Lp(M) → Lp(M) onto E with ‖P‖cb ≤ cp · n ̨̨ ̨ 1 2 − 1 p ̨̨ ̨ . We fo...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2003
ISSN: 0022-1236
DOI: 10.1016/s0022-1236(03)00045-4