Abstract
A non-zero vector-valued sequence u ∈ ℓq(X′) is a cover for a subset M of ℓP(X) if, for some 0 < α ≤ 1, ∥u * h∥ ∞ ≥ α ∥u∥q ∥h∥p for all h ∈ M. Covers of ℓ1 = ℓ1(R) are important in worst case system identification in ℓ1 and in the reconstruction of elements in a normed space from corrupted functional values. We investigate the existence of covers for certain naturally occurring subspaces of ℓp(X). We show that there exist finitely supported covers for some subspaces, and obtain lower bounds for their ’lengths’. We also obtain similar results for covers associated with convolution products for spaces of measurable vector-valued functions defined on the positive real axis.
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.
