Weak minimizing property on pairs of classical Banach spaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866909999861596160 |
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| author | Han, Manwook |
| author_facet | Han, Manwook |
| contents | We investigate the minimum modulus analogue of the weak maximizing property, termed the \emph{weak minimizing property}. We establish that the pairs $(\ell_p, L^p[0, 1])$ for $2 \leq p < \infty$ and $(\ell_s \oplus_q \ell_q, \ell_r \oplus_p \ell_p)$ for $1 < p \leq r\leq s \leq q < \infty$ satisfy the weak minimizing property. Conversely, we prove that the pairs $(\ell_1, \ell_p)$, $(\ell_1, c_0)$, $(\ell_1, \ell_1)$ and $(c_0, \ell_p)$ fail to satisfy the weak minimizing property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17316 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weak minimizing property on pairs of classical Banach spaces Han, Manwook Functional Analysis We investigate the minimum modulus analogue of the weak maximizing property, termed the \emph{weak minimizing property}. We establish that the pairs $(\ell_p, L^p[0, 1])$ for $2 \leq p < \infty$ and $(\ell_s \oplus_q \ell_q, \ell_r \oplus_p \ell_p)$ for $1 < p \leq r\leq s \leq q < \infty$ satisfy the weak minimizing property. Conversely, we prove that the pairs $(\ell_1, \ell_p)$, $(\ell_1, c_0)$, $(\ell_1, \ell_1)$ and $(c_0, \ell_p)$ fail to satisfy the weak minimizing property. |
| title | Weak minimizing property on pairs of classical Banach spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2601.17316 |