Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limited operators and differentiability   We characterize the limited operators by differentiability of convex
continuous functions. Given Banach spaces $Y$ and $X$ and a linear continuous
operator $T: Y \longrightarrow X$, we prove that $T$ is a limited operator if
and only if, for every convex continuous function $f: X \longrightarrow \R$ and
every point $y\in Y$, $f\circ T$ is Fr\'echet differentiable at $y\in Y$
whenever $f$ is G\^ateaux differentiable at $T(y)\in X$.

13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio