HOMOGENEOUS HILBERTIAN SUBSPACES OF NON-COMMUTATIVE Lp SPACES
نویسندگان
چکیده
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 Hilbertian subspace of a “commutative” space Lp(μ) (μ is a σ-finite measure) is completely isomorphic to the span of Rademacher functions in Lp([0, 1]).
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