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 Lp(μ, X) and Lq(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 Lp(μ, X), 1 ≤ p < ∞,also has Property H.
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.
基金
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)
