A Remark on the Stability of Approximative Compactness. (21st January 2016) - Luo, Zhenghua; Sun, Longfa; Zhang, Wen
Abstract : We study the stability of approximative τ -compactness, where τ is the norm or the weak topology. Let Λ be an index set and for every λ ∈ Λ, let Y λ be a subspace of a Banach space X λ . For 1 ≤ p < ∞, let X = ⊕ l p X λ and Y = ⊕ l p Y λ . We prove that Y (resp., B Y ) is approximatively τ -compact in X if and only if, for every λ ∈ Λ, Y λ (resp., B Y λ ) is approximatively τ -compact in X λ .