Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isometric factorization of vector measures and applications to spaces of
  integrable functions   Let $X$ be a Banach space, $\Sigma$ be a $\sigma$-algebra, and $m:\Sigma\to
X$ be a (countably additive) vector measure. It is a well known consequence of
the Davis-Figiel-Johnson-Pelcz\'{y}nski factorization procedure that there
exist a reflexive Banach space $Y$, a vector measure $\tilde{m}:\Sigma \to Y$
and an injective operator $J:Y \to X$ such that $m$ factors as $m=J\circ
\tilde{m}$. We elaborate some theory of factoring vector measures and their
integration operators with the help of the isometric version of the
Davis-Figiel-Johnson-Pelcz\'{y}nski factorization procedure. Along this way, we
sharpen a result of Okada and Ricker that if the integration operator on
$L_1(m)$ is weakly compact, then $L_1(m)$ is equal, up to equivalence of norms,
to some $L_1(\tilde m)$ where $Y$ is reflexive; here we prove that the above
equality can be taken to be isometric.

7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg