Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Common properties of bounded linear operators $AC$ and $BA$: Spectral
  theory   Let $X,Y$ be Banach spaces, $A:X \longrightarrow Y$ and $B,C:Y
\longrightarrow X$ be bounded linear operators satisfying operator equation
$ABA=ACA$. Recently, as extensions of Jacobson's lemma, Corach, Duggal and
Harte studied common properties of $AC-I$ and $BA-I$ in algebraic viewpoint and
also obtained some topological analogues. In this note, we continue to
investigate common properties of $AC$ and $BA$ from the viewpoint of spectral
theory. In particular, we give an affirmative answer to one question posed by
Corach et al. by proving that $AC - I$ has closed range if and only if $BA - I$
has closed range.

4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol