A Remark on the Stability of Approximative Compactness
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 Yλ be a subspace of a Banach space Xλ. For 1≤p<∞, let X=⊕lpXλ and Y=⊕lpYλ. We prove that Y (resp., BY) is approximatively τ-compact in X if and only if, fo...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/2734947 |
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| author | Zhenghua Luo Longfa Sun Wen Zhang |
| author_facet | Zhenghua Luo Longfa Sun Wen Zhang |
| author_sort | Zhenghua Luo |
| collection | DOAJ |
| description | 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 Yλ be a subspace of a Banach space Xλ. For 1≤p<∞, let X=⊕lpXλ and Y=⊕lpYλ. We prove that Y (resp., BY) is approximatively τ-compact in X if and only if, for every λ∈Λ, Yλ (resp., BYλ) is approximatively τ-compact in Xλ. |
| format | Article |
| id | doaj-art-b1d2c42d68c54571a56afeb8c8d349d5 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-b1d2c42d68c54571a56afeb8c8d349d52025-02-03T06:00:02ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/27349472734947A Remark on the Stability of Approximative CompactnessZhenghua Luo0Longfa Sun1Wen Zhang2School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, ChinaSchool of Mathematical Sciences, Xiamen University, Xiamen 361005, ChinaSchool of Mathematical Sciences, Xiamen University, Xiamen 361005, ChinaWe 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 Yλ be a subspace of a Banach space Xλ. For 1≤p<∞, let X=⊕lpXλ and Y=⊕lpYλ. We prove that Y (resp., BY) is approximatively τ-compact in X if and only if, for every λ∈Λ, Yλ (resp., BYλ) is approximatively τ-compact in Xλ.http://dx.doi.org/10.1155/2016/2734947 |
| spellingShingle | Zhenghua Luo Longfa Sun Wen Zhang A Remark on the Stability of Approximative Compactness Journal of Function Spaces |
| title | A Remark on the Stability of Approximative Compactness |
| title_full | A Remark on the Stability of Approximative Compactness |
| title_fullStr | A Remark on the Stability of Approximative Compactness |
| title_full_unstemmed | A Remark on the Stability of Approximative Compactness |
| title_short | A Remark on the Stability of Approximative Compactness |
| title_sort | remark on the stability of approximative compactness |
| url | http://dx.doi.org/10.1155/2016/2734947 |
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