Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unbounded operators: (square) roots, nilpotence, closability and some
  related invertibility results   In this paper, we are mainly concerned with studying arbitrary unbounded
square roots of linear operators as well as some of their basic properties. The
paper contains many examples and counterexamples. As an illustration, we give
explicit everywhere defined unbounded non-closable $nth$ roots of the identity
operator as well as the zero operator. We also show a non-closable unbounded
operator without any non-closable square root. Among other consequences, we
have a way of finding everywhere defined bijective operators, everywhere
defined operators which are surjective without being injective and everywhere
defined operators which are injective without being surjective. Some related
results on nilpotence are also given.

17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn