Acta Mathematica Sinica, English Series

, Volume 33, Issue 5, pp 681–690

Uniform homeomorphisms of unit spheres and Property H of Lebesgue–Bochner function spaces

Article

DOI: 10.1007/s10114-016-6245-1

Cite this article as:
Cheng, Q.J. & Dong, Y.B. Acta. Math. Sin.-English Ser. (2017) 33: 681. doi:10.1007/s10114-016-6245-1
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Abstract

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.

Keywords

Banach space uniform classification Property H Novikov conjecture 

MR(2010) Subject Classification

46B20 46B80 

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesXiamen UniversityXiamenP. R. China
  2. 2.School of Mathematics and ComputerWuhan Textile UniversityWuhanP. R. China

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