Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on triangular operators on Smooth Sequence Spaces   For a scalar sequence {(\theta_n)}_{n \in \mathbb{N}}, let C be the matrix
defined by c_n^k = \theta_{n-k+1} if n > k, c_n^k = 0 if n < k. The map between
K\"{o}the spaces \lambda(A) and \lambda(B) is called a Cauchy Product map if it
is determined by the triangular matrix C. In this note we introduced some
necessary and sufficient conditions for a Cauchy Product map on a nuclear
K\"{o}the space \lambda(A) to nuclear G_1-space \lambda(B) to be linear and
continuous. Its transpose is also considered.

34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th