Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The factorization property of $\ell^\infty(X_k)$   In this paper we consider the following problem: Let $X_k$, be a Banach space
with a normalized basis $(e_{(k,j)})_j$, whose biorthogonals are denoted by
$(e_{(k,j)}^*)_j$, for $k\in\mathbb{N}$, let
$Z=\ell^\infty(X_k:k\in\mathbb{N})$ be their $\ell^\infty$-sum, and let $T:Z\to
Z$ be a bounded linear operator, with a large diagonal, i.e. $$\inf_{k,j}
\big|e^*_{(k,j)}(T(e_{(k,j)})\big|>0.$$ Under which condition does the identity
on $Z$ factor through $T$? The purpose of this paper is to formulate general
conditions for which the answer is positive.

11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph