$\ell_1$ spreading models and the FPP for Cesàro mean nonexpansive maps
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913725978509312 |
|---|---|
| author | Barroso, C. S. |
| author_facet | Barroso, C. S. |
| contents | Let $K$ be a nonempty subset of a Banach space $X$. A mapping $T\colon K\to K$ is called $\mathfrak{cm}$-nonexpansive if for any sequence $(u_i)_{i=1}^\infty$ and $y$ in $K$, $\limsup_{i\to\infty} \sup_{A\subset\{1,\dots, n\}}\|\sum_{k\in A} \big(T u_{i+k} - Ty\big)\|\leq \limsup_{i\to\infty} \sup_{A\subset\{1,\dots, n\}}\|\sum_{k\in A} (u_{i+k} - y)\|$ for all $n\in\mathbb{N}$. As a subclass of the class of nonexpansive maps, its FPP is well-established in a wide variety of spaces. The main result of this paper is a fixed point result relating $\mathfrak{cm}$-nonexpansiveness, $\ell_1$ spreading models and Schauder bases with not-so-large basis constants. As a consequence, we deduce that Banach spaces with the weak Banach-Saks property have the fixed point property for $\mathfrak{cm}$-nonexpansive maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18113 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\ell_1$ spreading models and the FPP for Cesàro mean nonexpansive maps Barroso, C. S. Functional Analysis Let $K$ be a nonempty subset of a Banach space $X$. A mapping $T\colon K\to K$ is called $\mathfrak{cm}$-nonexpansive if for any sequence $(u_i)_{i=1}^\infty$ and $y$ in $K$, $\limsup_{i\to\infty} \sup_{A\subset\{1,\dots, n\}}\|\sum_{k\in A} \big(T u_{i+k} - Ty\big)\|\leq \limsup_{i\to\infty} \sup_{A\subset\{1,\dots, n\}}\|\sum_{k\in A} (u_{i+k} - y)\|$ for all $n\in\mathbb{N}$. As a subclass of the class of nonexpansive maps, its FPP is well-established in a wide variety of spaces. The main result of this paper is a fixed point result relating $\mathfrak{cm}$-nonexpansiveness, $\ell_1$ spreading models and Schauder bases with not-so-large basis constants. As a consequence, we deduce that Banach spaces with the weak Banach-Saks property have the fixed point property for $\mathfrak{cm}$-nonexpansive maps. |
| title | $\ell_1$ spreading models and the FPP for Cesàro mean nonexpansive maps |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2403.18113 |