Strong peak points and strongly norm attaining points with applications to denseness and polynomial numerical indices
| dc.creator | Kim, Jaegil | |
| dc.creator | Lee, Han Ju | |
| dc.date | 2008-06-03 | |
| dc.date.accessioned | 2026-07-07T09:42:25Z | |
| dc.date.available | 2026-07-07T09:42:25Z | |
| dc.description | Using the variational method, it is shown that the set of all strong peak functions in a closed algebra $A$ of $C_b(K)$ is dense if and only if the set of all strong peak points is a norming subset of $A$. As a corollary we can induce the denseness of strong peak functions on other certain spaces. In case that a set of uniformly strongly exposed points of a Banach space $X$ is a norming subset of $\mathcal{P}({}^n X)$, then the set of all strongly norm attaining elements in $\mathcal{P}({}^n X)$ is dense. In particular, the set of all points at which the norm of $\mathcal{P}({}^n X)$ is Fréchet differentiable is a dense $G_δ$ subset. In the last part, using Reisner's graph theoretic-approach, we construct some strongly norm attaining polynomials on a CL-space with an absolute norm. Then we show that for a finite dimensional complex Banach space $X$ with an absolute norm, its polynomial numerical indices are one if and only if $X$ is isometric to $\ell_\infty^n$. Moreover, we give a characterization of the set of all complex extreme points of the unit ball of a CL-space with an absolute norm. | |
| dc.identifier | https://arxiv.org/abs/0806.0507 | |
| dc.identifier | http://arxiv.org/abs/0806.0507 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162173 | |
| dc.subject | Functional Analysis | |
| dc.subject | Combinatorics | |
| dc.subject | 46G25; 46B20; 46B22; 52A21; 46B20 | |
| dc.title | Strong peak points and strongly norm attaining points with applications to denseness and polynomial numerical indices | |
| dc.type | text |