Open AccessThe continuity and the simplest possible expression of inner inverses of linear operators in Banach space
Author(s) -
Saijie Chen,
Yayuan Zhao,
L. Zhu,
Qianglian Huang
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2104241c
Subject(s) - mathematics , invertible matrix , inverse , expression (computer science) , banach space , equivalence (formal languages) , pure mathematics , inner product space , operator (biology) , sequence (biology) , geometry , chemistry , biochemistry , repressor , computer science , transcription factor , gene , programming language
The main topic of this paper is the relationship between the continuity and the simplest possible expression of inner inverses. We first provide some new characterizations for the simplest possible expression to be an inner inverse of the perturbed operator. Then we obtain the equivalence conditions on the continuity of the inner inverse. Furthermore, we prove that if Tn ? T and the sequence of inner inverses {T?n} is convergent, then T is inner invertible and we can find a succinct expression of the inner inverse of Tn, which converge to any given inner inverse T?. This is very useful and convenient in applications.