Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability constants of the weak$^*$ fixed point property for the space
  $\ell_1$   The main aim of the paper is to study some quantitative aspects of the
stability of the weak$^*$ fixed point property for nonexpansive maps in
$\ell_1$ (shortly, $w^*$-fpp). We focus on two complementary approaches to this
topic. First, given a predual $X$ of $\ell_1$ such that the
$\sigma(\ell_1,X)$-fpp holds, we precisely establish how far, with respect to
the Banach-Mazur distance, we can move from $X$ without losing the $w^*$-fpp.
The interesting point to note here is that our estimate depends only on the
smallest radius of the ball in $\ell_1$ containing all
$\sigma(\ell_1,X)$-cluster points of the extreme points of the unit ball.
Second, we pass to consider the stability of the $w^*$-fpp in the restricted
framework of preduals of $\ell_1$. Namely, we show that every predual $X$ of
$\ell_1$ with a distance from $c_0$ strictly less than $3$, induces a weak$^*$
topology on $\ell_1$ such that the $\sigma(\ell_1,X)$-fpp holds.

34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph