Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Further results on the $(b, c)$-inverse, the outer inverse $A^{(2)}_{T,
  S}$ and the Moore-Penrose inverse in the Banach context   In this article properties of the $(b, c)$-inverse, the inverse along an
element, the outer inverse with prescribed range and null space $A^{(2)}_{T,
S}$ and the Moore-Penrose inverse will be studied in the contexts of Banach
spaces operators, Banach algebras and $C^*$-algebras. The main properties to be
considered are the continuity, the differentiability and the openness of the
sets of all invertible elements defined by all the aforementioned outer
inverses but the Moore-Penrose inverse. The relationship between the $(b,
c)$-inverse and the outer inverse $A^{(2)}_{T, S}$ will be also characterized.

22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an