Abstract
For any Hilbert spaces H1 and H2, let B(H1,H2) be the set of bounded linear operators from H1 to H2. In this paper, necessary and sufficient conditions are given under which an anti-triangular block operator matrix E=(ABC0) is group invertible, where A∈B(H1,H1),B∈B(H2,H1) and C∈B(H1,H2). In the case that E is group invertible, a new formula for the group inverse of E is derived under the only restriction that certain associated operators have closed ranges. This gives especially a new characterization of the group inverse of an anti-triangular block matrix without restrictions on its individual block matrices.
Sign-in/Register to access full text options 
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.
