Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completness of roots elementes of linear operators in Banach spaces and
  application   In this paper the general spectral properties of linear operators in Banach
spaces are studied. We find sufficient conditions on structure of Banach spaces
and resolvent properties that guarantee completeness of roots elements of
Schatten class operators. This approach generalizes the well known result for
operators in Hilbert spaces. In application, the boundary value problems for
the abstract equation of second order with variable coefficients are studied.
The principal part of the appropriate differential operator is not
self-adjoint. The discreetness of spectrum and completeness of root elements of
this operator are obtained.

24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics