Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally convex spaces and Schur type properties   In the main result of the paper we extend Rosenthal's characterization of
Banach spaces with the Schur property by showing that for a quasi-complete
locally convex space $E$ whose separable bounded sets are metrizable the
following conditions are equivalent: (1) $E$ has the Schur property, (2) $E$
and $E_w$ have the same sequentially compact sets, where $E_w$ is the space $E$
with the weak topology, (3) $E$ and $E_w$ have the same compact sets, (4) $E$
and $E_w$ have the same countably compact sets, (5) $E$ and $E_w$ have the same
pseudocompact sets, (6) $E$ and $E_w$ have the same functionally bounded sets,
(7) every bounded non-precompact sequence in $E$ has a subsequence which is
equivalent to the unit basis of $\ell_1$ and (8) every bounded non-precompact
sequence in $E$ has a subsequence which is discrete and $C$-embedded in $E_w$.

17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci