Strong peak points and denseness of strong peak functions
| dc.creator | Lee, Han Ju | |
| dc.date | 2007-05-18 | |
| dc.date.accessioned | 2026-07-07T08:02:13Z | |
| dc.date.available | 2026-07-07T08:02:13Z | |
| dc.description | Let $C_b(K)$ be the set of all bounded continuous (real or complex) functions on a complete metric space $K$ and $A$ a closed subspace of $C_b(K)$. Using the variational method, it is shown that the set of all strong peak functions in $A$ is dense if and only if the set of all strong peak points is a norming subset of $A$. As a corollary we show that if $X$ is a locally uniformly convex, complex Banach space, then the set of all strong peak functions in $\mathcal{A}(B_X)$ is a dense $G_δ$ subset. Moreover if $X$ is separable, smooth and locally uniformly convex, then the set of all norm and numerical strong peak functions in $\mathcal{A}_u(B_X:X)$ is a dense $G_δ$ subset. In case that a set of uniformly strongly exposed points of a (real or complex) Banach space $X$ is a norming subset of $\mathcal{P}({}^n X)$ for some $n\ge 1$, 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. | |
| dc.identifier | https://arxiv.org/abs/0705.2650 | |
| dc.identifier | http://arxiv.org/abs/0705.2650 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129162 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B04, 46G20, 46G25, 46B22 | |
| dc.title | Strong peak points and denseness of strong peak functions | |
| dc.type | text |