Abstract

Given a Banach lattice E and a Banach space Y we say that a bounded linear operator T : E → Y is lattice strictly singular (disjointly strictly singular) if it fails to be invertible on any infinite-dimensional sublattice of E (on the span of any pairwise disjoint sequence in E). This is a survey on the existing answers up to the present day to the following questions: Is every lattice strictly singular operator also disjointly strictly singular? Do lattice strictly singular operators have a vector space structure?

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 call

Disclaimer: 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.