In this paper,for 1<p<∞,the authors show that the coarse l^(p)-Novikov conjecture holds for metric spaces with bounded geometry which are coarsely embeddable into a Banach space with Kasparov-Yu’s 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 Lp(μ, X) and Lq(μ, Y)are mutually uniformly homeomorphic ...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.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12171156)the Science and Technology Commission of Shanghai Municipality(No.22DZ2229014)。
文摘In this paper,for 1<p<∞,the authors show that the coarse l^(p)-Novikov conjecture holds for metric spaces with bounded geometry which are coarsely embeddable into a Banach space with Kasparov-Yu’s 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)
文摘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.
