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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)… Click to show full 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:
unit;
function spaces;
property;
unit spheres;
bochner function;
lebesgue bochner
Journal Title: Acta Mathematica Sinica, English Series
Year Published: 2017
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Journal Title: Acta Mathematica Sinica, English Series
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!