Abstract
AbstractWe define and studyλ-strict ideals in Banach spaces, which forλ=1 means strict ideals. Strict u-ideals in their biduals are known to have the unique ideal property; we prove that so also doλ-strict u-ideals in their biduals, at least forλ>1/2. An open question, posed by Godefroyet al. [‘Unconditional ideals in Banach spaces’,Studia Math.104(1993), 13–59] is whether the Banach spaceXis a u-ideal in Ba(X), the Baire-one functions inX**, exactly whenκu(X)=1; we prove that ifκu(X)=1 thenXis a strict u-ideal in Ba (X) , and we establish the converse in the separable case.
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.
