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Uniform homeomorphisms between the unit balls in $ L\sb p$ and $ l\sb p$


Author: Gun-Marie Lövblom
Journal: Proc. Amer. Math. Soc. 123 (1995), 405-409
MSC: Primary 46B99; Secondary 46B25, 46E30
MathSciNet review: 1227523
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Abstract: Let $ T:B({L_p}) \to B({l_p}),1 \leq p < 2$, be a uniform homeomorphism with modulus of continuity $ {\delta _T}$. It is shown that for any $ \gamma ,0 \leq \gamma < \frac{{2 - p}}{{2p}}$, there exists $ K > 0$ and a sequence $ \{ {\varepsilon _n}\} $ with $ {\varepsilon _n} \to 0$ such that $ \delta _T^{ - 1}({\delta _T}({\varepsilon _n})) \geq K{\varepsilon _n}\vert\log {\varepsilon _n}{\vert^\gamma }$ for all $ {\varepsilon _n}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1227523-8
Article copyright: © Copyright 1995 American Mathematical Society