TY - JOUR
T1 - On Banach spaces with Kasparov and Yu's Property (H)
AU - Cheng, Qingjin
AU - Wang, Qin
N1 - Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - A new geometric property of Banach spaces recently introduced by G. Kasparov and G. Yu, called Property (H), has important applications to the strong Novikov conjecture and the coarse Novikov conjecture, yet is far from being well understood. In this paper, we investigate various uniformly continuous maps on unit spheres of Banach spaces and prove that all separable Banach lattices with nontrivial cotype have Property (H).
AB - A new geometric property of Banach spaces recently introduced by G. Kasparov and G. Yu, called Property (H), has important applications to the strong Novikov conjecture and the coarse Novikov conjecture, yet is far from being well understood. In this paper, we investigate various uniformly continuous maps on unit spheres of Banach spaces and prove that all separable Banach lattices with nontrivial cotype have Property (H).
KW - Banach lattices
KW - Geometry of Banach spaces
KW - Kasparov–Yu's Property (H)
KW - The Novikov conjecture
UR - https://www.scopus.com/pages/publications/85027968676
U2 - 10.1016/j.jmaa.2017.08.005
DO - 10.1016/j.jmaa.2017.08.005
M3 - 文章
AN - SCOPUS:85027968676
SN - 0022-247X
VL - 457
SP - 200
EP - 213
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -