A Remark on the Stability of Approximative Compactness. (21st January 2016)

• Record Type: Journal Article
• Authors: Luo, Zhenghua; Sun, Longfa; Zhang, Wen
• Other Names: Marino Giuseppe Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2016(2016)
• Publication Date: 2016-01-21
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2016/2734947
• Languages: English
• ISSNs: 2314-8896

Abstract

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 .