منابع مشابه
SMALL SUBSPACES OF Lp
We prove that if X is a subspace of Lp (2 < p < ∞), then either X embeds isomorphically into `p ⊕ `2 or X contains a subspace Y, which is isomorphic to `p(`2). We also give an intrinsic characterization of when X embeds into `p⊕`2 in terms of weakly null trees in X or, equivalently, in terms of the “infinite asymptotic game” played in X. This solves problems concerning small subspaces of Lp ori...
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We discuss the finite dimensional structure theory of L p ; in particular, the theory of restricted invertibility and classification of subspaces of ℓ n p .
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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: St. Petersburg Mathematical Journal
سال: 2008
ISSN: 1061-0022
DOI: 10.1090/s1061-0022-08-01001-7