Abstract
In this paper we characterize diagonal operators from ZP into l,, 1 <p, q < co, by their entropy numbers. The results contain those of Marcus [ 161 formulated in the language of c-entropy and Oloff [21]. Moreover, the remaining gaps in [ 16, 2 I] are tilled in the much more complicated situation where l<p<q<co. Furthermore, we extend the results to diagonal operators acting between Lorentz sequence spaces. It turns out that the computation of entropy numbers of diagonal operators can be reduced to the computation of certain entropy quasi-ideal norms of identity operators acting between the simple itdimensional vector spaces I;. Finally, the entropy numbers are used for studying eigenvalue problems of factorable operators acting on Banach spaces. The statements of this paper are obtained using results and techniques recently proved and developed by the author in [4].
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.
