Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
