南开大学学报(自然科学版) ›› 2023 ›› Issue (5): 59-.

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线性同构下有界函数空间的球覆盖性质(英文)

  

  • 出版日期:2023-10-20 发布日期:2023-10-30

  • Online:2023-10-20 Published:2023-10-30

摘要:

A normed vector space has the ball-covering property if its unit sphere can be covered by countably many closed balls off the origin. Two new examples, Cb (R) and L∞ (R), are considered by introducing new but equivalent norms (| ? |a and || ? ||λ) of them. (Cb (R),| ? |a) has the ball-covering property if and only if a ∈ (1/2,1 ]. And for all λ ∈ [ 0,1 ], (L∞ (R),? λ) fails the ball-covering property.

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