Guardat en:
| Autors principals: | , |
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| Format: | Preprint |
| Publicat: |
2025
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/2506.17762 |
| Etiquetes: |
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- In this paper, we study the Bishop-Phelps-Bollobás property for operators (BPBp for short). To this end, we investigate the generalized approximate hyperplane series property (generalized AHSP for short) for a pair $(X,Y)$ of Banach spaces, which characterizes when $(\ell_1(X),Y)$ has the BPBp. We prove the following results. For a locally compact Hausdorff space $L$, if $(X, \mathcal{C}_0(L,Y))$ has the BPBp, then so does $(X,Y)$. Furthermore, if the pair $(X, Y)$ has the generalized AHSP and $\mathcal{L}(X,Z) = \mathcal{K}(X,Z)$, then the pair $(X, Z)$ also has the generalized AHSP, where $Z$ is one of the spaces $\mathcal{C}(K, Y)$, $\mathcal{C}_0(L, Y)$, or $\mathcal{C}_b(Ω, Y)$, with $K$ a compact Hausdorff space and $Ω$ a completely regular space.