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| Uniform Homeomorphisms of Unit Spheres and Property H of Lebesgue–Bochner Function Spaces | |
| 基金项目： | The first author is supported by National Natural Science Foundation of China (Grant No. 11471271); the second author is supported by the Foundation of Hubei Provincial Department of Education (Grant No. Q20161602) |
| 摘 要： | Assume that the unit spheres of Banach spaces X and Y are uniformly homeomorphic.Then we prove that all unit spheres of the Lebesgue–Bochner function spaces L_p(μ, X) and L_q(μ, Y)are mutually uniformly homeomorphic where 1 ≤ p, q ∞. As its application, we show that if a Banach space X has Property H introduced by Kasparov and Yu, then the space L_p(μ, X), 1 ≤ p ∞,also has Property H. |
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