Abstract
Let [Formula: see text] be the algebra of all bounded linear operators on an infinite-dimensional complex or real Banach space [Formula: see text]. We prove that a bijective bicontinuous map [Formula: see text] on [Formula: see text] preserves the difference of group invertible operators in both directions if and only if [Formula: see text] is either of the form [Formula: see text] or of the form [Formula: see text], where [Formula: see text] is a nonzero scalar, [Formula: see text] and [Formula: see text] are two bounded invertible linear or conjugate linear operators.
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.
