A Remark on the Stability of Approximative Compactness. (21st January 2016) - Luo, Zhenghua; Sun, Longfa; Zhang, Wen
Abstract : We study the stability of approximativeτ -compactness, whereτ is the norm or the weak topology. LetΛ be an index set and for everyλ ∈ Λ, letY λ be a subspace of a Banach spaceX λ . For1 ≤ p < ∞, letX = ⊕ l p X λ andY = ⊕ l p Y λ . We prove thatY (resp., B Y ) is approximativelyτ -compact inX if and only if, for everyλ ∈ Λ, Y λ (resp., B Y λ ) is approximativelyτ -compact inX λ .