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Journal of Function Spaces
Volume 2016, Article ID 2734947, 5 pages
Research Article

A Remark on the Stability of Approximative Compactness

1School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
2School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received 26 November 2015; Accepted 12 January 2016

Academic Editor: Giuseppe Marino

Copyright © 2016 Zhenghua Luo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the stability of approximative -compactness, where is the norm or the weak topology. Let be an index set and for every let be a subspace of a Banach space . For , let and . We prove that (resp., ) is approximatively -compact in if and only if, for every , (resp., ) is approximatively -compact in .