Lipschitz extension constants equal projection constants
| dc.creator | Rieffel, Marc A. | |
| dc.date | 2005-08-04 | |
| dc.date | 2006-03-20 | |
| dc.date.accessioned | 2026-07-07T07:44:28Z | |
| dc.date.available | 2026-07-07T07:44:28Z | |
| dc.description | For a Banach space $V$ we define its Lipschitz extension constant, $\cL\cE(V)$, to be the infimum of the constants $c$ such that for every metric space $(Z,ρ)$, every $X \subset Z$, and every $f: X \to V$, there is an extension, $g$, of $f$ to $Z$ such that $L(g) \le cL(f)$, where $L$ denotes the Lipschitz constant. The basic theorem is that when $V$ is finite-dimensional we have $\cL\cE(V) = \cP\cC(V)$ where $\cP\cC(V)$ is the well-known projection constant of $V$. We obtain some direct consequences of this theorem, especially when $V = M_n(\bC)$. We then apply techniques for calculating projection constants, involving averaging projections, to calculate $\cL\cE((M_n(\bC))^{sa})$. We also discuss what happens if we also require that $\|g\|_{\infty} = \|f\|_{\infty}$. | |
| dc.description | 16 pages. Three very minor mathematical typos corrected. Intended for the proceedings of GPOTS05 | |
| dc.identifier | https://arxiv.org/abs/math/0508097 | |
| dc.identifier | http://arxiv.org/abs/math/0508097 | |
| dc.identifier | Contemporary Math. 414 (2006) 147-162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123210 | |
| dc.subject | Functional Analysis | |
| dc.subject | Metric Geometry | |
| dc.subject | 46B20; 26A16 | |
| dc.title | Lipschitz extension constants equal projection constants | |
| dc.type | text |