On stability of restricted center properties and continuity of restricted center map under $\ell_p$-direct sum
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915530802200576 |
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| author | P, Gayathri Thota, V |
| author_facet | P, Gayathri Thota, V |
| contents | We study the stability of various restricted center properties and certain continuity properties of the restricted center map. We observe that restricted center property, property-$(P_1)$ and semi-continuity properties of the restricted center map are preserved under $\ell_p$-direct sum $(1 \leq p < \infty).$ It is shown that property-$(P_2)$ is stable under finite $\ell_p$-direct sum, but not under infinite $\ell_p$-direct sum. Additionally, we introduce a notion called property-$(lP_2)$ as a sufficient condition for the continuity of the restricted center map. Further, the stability of property-$(lP_2)$ is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01955 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On stability of restricted center properties and continuity of restricted center map under $\ell_p$-direct sum P, Gayathri Thota, V Functional Analysis 41A65, 46B20 We study the stability of various restricted center properties and certain continuity properties of the restricted center map. We observe that restricted center property, property-$(P_1)$ and semi-continuity properties of the restricted center map are preserved under $\ell_p$-direct sum $(1 \leq p < \infty).$ It is shown that property-$(P_2)$ is stable under finite $\ell_p$-direct sum, but not under infinite $\ell_p$-direct sum. Additionally, we introduce a notion called property-$(lP_2)$ as a sufficient condition for the continuity of the restricted center map. Further, the stability of property-$(lP_2)$ is established. |
| title | On stability of restricted center properties and continuity of restricted center map under $\ell_p$-direct sum |
| topic | Functional Analysis 41A65, 46B20 |
| url | https://arxiv.org/abs/2510.01955 |