Uniform Homeomorphisms of Unit Spheres and Property H of Lebesgue–Bochner Function Spaces  

作　　者：Qing Jin CHENG Yun Bai DONG 

机构地区：[1]School of Mathematical Sciences,Xiamen University [2]School of Mathematics and Computer,Wuhan Textile University

出　　处：《Acta Mathematica Sinica,English Series》2017年第5期681-690,共10页数学学报（英文版）

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)

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.

关 键 词：Banach space uniform classification Property H Novikov conjecture 

分 类 号：O177.2[理学—数学]