Abstract
It is shown that if E is an infinite dimensional Banach space with first dual Eâ, second dual E", and nth dual E [ n ] {E^{[n]}} and if E [ n ] {E^{[n]}} is either an L- or M-space all duals are either L- or M-spaces except possibly E which could be a Lindenstrauss space. If E is an L- or M-space there is an integer n ( E ) n(E) so that if m > n ( E ) m > n(E) there is no Banach space F with E = F [ m ] E = {F^{[m]}} . The linear isomorphic analogues to these isometric results are also established. In particular if E is an L 1 {\mathcal {L}_1} or L â {\mathcal {L}_\infty } space there is an integer n ÂŻ ( E ) \bar n(E) so that E is not linearly isomorphic to F [ m ] {F^{[m]}} for any Banach space F when m > n ÂŻ ( E ) m > \bar n(E) .
Published Version (
Free)
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.
