Infinite dimensional spaces consisting of sequences that do not converge to zero
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912361997139968 |
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| author | Aires, Mikaela Botelho, Geraldo |
| author_facet | Aires, Mikaela Botelho, Geraldo |
| contents | Given a map $f \colon E \longrightarrow F$ between Banach spaces (or Banach lattices), a set $A$ of $E$-valued bounded sequences, ${\bf x} \in A$ and a vector topology $τ$ on $F$, we investigate the existence of an infinite dimensional Banach space (or Banach lattice) containing a subsequence of ${\bf x}$ and consisting, up to the origin, of sequences $(x_j)_{j=1}^\infty$ belonging to $A$ such that $(f(x_j))_{j=1}^\infty$ does not converge to zero with respect to $τ$. The applications we provide encompass the improvement of known results, as well as new results, concerning Banach spaces/Banach lattices not satisfying classical properties and linear/nonlinear maps not belonging to well studied classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03041 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite dimensional spaces consisting of sequences that do not converge to zero Aires, Mikaela Botelho, Geraldo Functional Analysis 46B42, 46B87, 47B07, 47H60 Given a map $f \colon E \longrightarrow F$ between Banach spaces (or Banach lattices), a set $A$ of $E$-valued bounded sequences, ${\bf x} \in A$ and a vector topology $τ$ on $F$, we investigate the existence of an infinite dimensional Banach space (or Banach lattice) containing a subsequence of ${\bf x}$ and consisting, up to the origin, of sequences $(x_j)_{j=1}^\infty$ belonging to $A$ such that $(f(x_j))_{j=1}^\infty$ does not converge to zero with respect to $τ$. The applications we provide encompass the improvement of known results, as well as new results, concerning Banach spaces/Banach lattices not satisfying classical properties and linear/nonlinear maps not belonging to well studied classes. |
| title | Infinite dimensional spaces consisting of sequences that do not converge to zero |
| topic | Functional Analysis 46B42, 46B87, 47B07, 47H60 |
| url | https://arxiv.org/abs/2505.03041 |