Ball-covering property of Banach spaces that is not preserved under linear isomorphisms |
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基金项目: | Supported by the National Natural Science Foundation of China (Grant No. 10471114) |
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摘 要: | By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ball-covering property, if it admits a ball-covering consisting of countably many balls. This paper, by constructing the equivalent norms on l~∞, shows that ball-covering property is not invariant under isomorphic mappings, though it is preserved under such mappings if X is a Gateaux differentiability space; presents that this property of X is not heritable by its closed subspaces; and the property is also not preserved under quotient mappings.
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收稿时间: | 27 February 2007 |
修稿时间: | 19 April 2007 |
Ball-covering property of Banach spaces that is not preserved under linear isomorphisms |
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Authors: | Cheng LiXin Cheng QingJin and Liu XiaoYan |
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Institution: | (1) Department of Mathematics, Xiamen University, Xiamen, 361005, China |
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Abstract: | By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ball-covering property, if it admits a ball-covering consisting of countably many balls. This paper, by
constructing the equivalent norms on l
∞, shows that ball-covering property is not invariant under isomorphic mappings, though it is preserved under such mappings
if X is a Gateaux differentiability space; presents that this property of X is not heritable by its closed subspaces; and the property is also not preserved under quotient mappings.
Supported by the National Natural Science Foundation of China (Grant No. 10471114) |
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Keywords: | ball-covering isomorphic invariant Gateaux differentiability space Banach space |
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