Nonlinear structure of some classical quasi-Banach spaces and -spaces |
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Authors: | F Albiac |
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Institution: | aDepartment of Mathematics, University of Missouri, Columbia, MO 65211, USA;bDepartamento de Matemáticas, Universidad Pública de Navarra, Pamplona 31006, Spain |
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Abstract: | We investigate the Lipschitz structure of ℓp and Lp for 0<p<1 as quasi-Banach spaces and as metric spaces (with the metric induced by the p-norm) and show that they are not Lipschitz isomorphic. We prove that the -space L0 is not uniformly homeomorphic to any other Lp space, that the Lp spaces for 0<p<1 embed isometrically into one another, and reduce the problem of the uniform equivalence amongst Lp spaces to their Lipschitz equivalence as metric spaces. |
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Keywords: | Banach space ![](http://www&prev_q=<a name=) ![](http://www) sciencedirect -space" target="_blank">com/cache/MiamiImageURL/B6WK2-4PT29C7-1-4/0?wchp=dGLbVlb-zSkWz" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=11 width="10"/>-space Uniform homeomorphism Lipschitz |
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