Total sequences and the lower frame inequality
Narutaka Ozawa
TL;DR
This paper proves that any total sequence in a Hilbert space can be scaled to satisfy the lower frame inequality, addressing a problem posed by A. Kulikov.
Contribution
It establishes that all total sequences in Hilbert spaces can be scaled to meet the lower frame inequality, solving a previously posed open problem.
Findings
Every total sequence can be scaled to satisfy the lower frame inequality
Addresses and resolves a problem posed on mathoverflow
Advances understanding of frame theory in Hilbert spaces
Abstract
We prove that every total sequence in a Hilbert space satisfies the lower frame inequality after scaling. This solves A. Kulikov's "exercise" at mathoverflow.
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Taxonomy
TopicsAdvanced Banach Space Theory · Holomorphic and Operator Theory · Mathematical Analysis and Transform Methods