Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost everywhere convergent sequences of weak$^*$-to-norm continuous
  operators   Let $X$ and $Y$ be Banach spaces, and $T:X^*\to Y$ be an operator. We prove
that if $X$ is Asplund and $Y$ has the approximation property, then for each
Radon probability $\mu$ on $(B_{X^*},w^*)$ there is a sequence of $w^*$-to-norm
continuous operators $T_n:X^*\to Y$ such that $\|T_n(x^*)-T(x^*)\| \to 0$ for
$\mu$-a.e. $x^*\in B_{X^*}$; if $Y$ has the $\lambda$-bounded approximation
property for some $\lambda\geq 1$, then the sequence can be chosen in such a
way that $\|T_n\|\leq \lambda\|T\|$ for all $n\in \mathbb{N}$. The same
conclusions hold if $X$ contains no subspace isomorphic to $\ell_1$, $Y$ has
the approximation property (resp., $\lambda$-bounded approximation property)
and $T$ has separable range. This extends to the non-separable setting a result
by Mercourakis and Stamati.

36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat