The geometry of $L_0$
| dc.creator | Kalton, N. J. | |
| dc.creator | Koldobsky, A. | |
| dc.creator | Yaskin, V. | |
| dc.creator | Yaskina, M. | |
| dc.date | 2004-12-19 | |
| dc.date.accessioned | 2026-07-07T05:15:26Z | |
| dc.date.available | 2026-07-07T05:15:26Z | |
| dc.description | Suppose that we have the unit Euclidean ball in $\R^n$ and construct new bodies using three operations - linear transformations, closure in the radial metric and multiplicative summation defined by $\|x\|_{K+_0L} = \sqrt{\|x\|_K\|x\|_L}.$ We prove that in dimension 3 this procedure gives all origin symmetric convex bodies, while this is no longer true in dimensions 4 and higher. We introduce the concept of embedding of a normed space in $L_0$ that naturally extends the corresponding properties of $L_p$-spaces with $p\ne0$, and show that the procedure described above gives exactly the unit balls of subspaces of $L_0$ in every dimension. We provide Fourier analytic and geometric characterizations of spaces embedding in $L_0$, and prove several facts confirming the place of $L_0$ in the scale of $L_p$-spaces. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0412371 | |
| dc.identifier | http://arxiv.org/abs/math/0412371 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73630 | |
| dc.subject | Functional Analysis | |
| dc.subject | Metric Geometry | |
| dc.subject | 46B20, 52Axx | |
| dc.title | The geometry of $L_0$ | |
| dc.type | text |