Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complemented basic sequences in Frechet spaces with finite dimensional
  decomposition   Let $E$ be a Frechet-Montel space and $(E_n)_{n \in \mathbb{N}}$ be a finite
dimensional unconditional decomposition of $E$ with $\dim(E_n)\leq k$ for some
fixed $k \in \mathbb{N}$ and for all $n \in \mathbb{N}$. Consider a sequence
$(x_n)_{n \in \mathbb{N}}$ formed by taking an element $x_n$ from each $E_n$
for all $n \in \mathbb{N}$. Then $(x_n)_{n \in \mathbb{N}}$ has a subsequence
which is complemented in $E$

33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph