The Strong Property (B) for Lp Spaces
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Given a purely non-atomic, finite measure space (Ω, Σ, ν), it is proved that for every closed, infinite-dimensional subspace V of Lp(ν) (1 ≤ p < ∞) there exists a decomposition Lp(ν) = X1 ⊕ X2, such that both subspaces X1 and X2 are isomorphic to Lp(ν) and both V ∩X1 and V ∩ X2 are infinite-dimensional. Some consequences concerning dense, non-closed range operators on L1 are derived
Given a purely non-atomic, finite measure space (Ω, Σ, ν), it is proved that for every closed, infinite-dimensional subspace V of Lp(ν) (1 ≤ p < ∞) there exists a decomposition Lp(ν) = X1 ⊕ X2, such that both subspaces X1 and X2 are isomorphic to Lp(ν) and both V ∩X1 and V ∩ X2 are infinite-dimensional. Some consequences concerning dense, non-closed range operators on L1 are derived
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