On the intrinsic and the spatial numerical range
| dc.creator | Martin, Miguel | |
| dc.creator | Meri, Javier | |
| dc.creator | Paya, Rafael | |
| dc.date | 2005-03-04 | |
| dc.date.accessioned | 2026-07-07T05:17:39Z | |
| dc.date.available | 2026-07-07T05:17:39Z | |
| dc.description | For a bounded function $f$ from the unit sphere of a closed subspace $X$ of a Banach space $Y$, we study when the closed convex hull of its spatial numerical range $W(f)$ is equal to its intrinsic numerical range $V(f)$. We show that for every infinite-dimensional Banach space $X$ there is a superspace $Y$ and a bounded linear operator $T:X\longrightarrow Y$ such that $\bar{co} W(T)\neq V(T)$. We also show that, up to renormig, for every non-reflexive Banach space $Y$, one can find a closed subspace $X$ and a bounded linear operator $T\in L(X,Y)$ such that $\bar{co} W(T)\neq V(T)$. Finally, we introduce a sufficient condition for the closed convex hull of the spatial numerical range to be equal to the intrinsic numerical range, which we call the Bishop-Phelps-Bollobas property, and which is weaker than the uniform smoothness and the finite-dimensionality. We characterize strong subdifferentiability and uniform smoothness in terms of this property. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0503076 | |
| dc.identifier | http://arxiv.org/abs/math/0503076 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74384 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B20; 47A12 | |
| dc.title | On the intrinsic and the spatial numerical range | |
| dc.type | text |