Abstract
A Hilbert space operator A is said to be core invertible if it has an inner inverse whose range coincides with the range of A and whose null space coincides with the null space of the adjoint of A. This notion was introduced by Baksalary, Trenkler, Rakić, Dinčić, and Djordjević in the last decade, who also proved that core invertibility is equivalent to group invertibility and that the core and group inverses coincide if and only if A is a so-called EP operator. The present paper contains criteria for core invertibility and for the EP property as well as formulas for the core inverse for operators in the von Neumann algebra generated by two orthogonal projections.
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.
