Weak cluster points of maximizing sequences on Banach spaces satisfying $\boldsymbol{(M_p)}$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917292446580736 |
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| author | Norrbo, David |
| author_facet | Norrbo, David |
| contents | Given a bounded linear operator $T$ on a separable Banach space with property $(M_p)$, we prove that the smallest and the largest norm of weak cluster points of all maximizing sequences for $T$ can only take the values $0$ or $1$. The three classes of bounded linear operators emerging from the dichotomy of these extremal norm values coincides with the partition, created by considering the norm-attaining property and if the essential norm equals the norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11420 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak cluster points of maximizing sequences on Banach spaces satisfying $\boldsymbol{(M_p)}$ Norrbo, David Functional Analysis 47B01, 47A30 (Primary) 46B20, 47B37, 47L05, 46B10 (Secondary) Given a bounded linear operator $T$ on a separable Banach space with property $(M_p)$, we prove that the smallest and the largest norm of weak cluster points of all maximizing sequences for $T$ can only take the values $0$ or $1$. The three classes of bounded linear operators emerging from the dichotomy of these extremal norm values coincides with the partition, created by considering the norm-attaining property and if the essential norm equals the norm. |
| title | Weak cluster points of maximizing sequences on Banach spaces satisfying $\boldsymbol{(M_p)}$ |
| topic | Functional Analysis 47B01, 47A30 (Primary) 46B20, 47B37, 47L05, 46B10 (Secondary) |
| url | https://arxiv.org/abs/2508.11420 |