3 problems

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The quantitative $R_\epsilon$ -conjecture for finite Riesz basic sequences
Quantitative $R_\epsilon$ -conjecture. There is a natural number $r=r(\epsilon,A,B)$ such that, for every $n\in\mathbb N$ and every such sequence, there is a partition…
Conjectureopenfunctional-analysis kadison-singer riesz-sequencesarXiv posted 2 days ago
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The $R_\epsilon$ -conjecture for unit norm Riesz basic sequences
$R_\epsilon$ -conjecture. Every unit norm Riesz basic sequence is a finite union of $\epsilon$ -Riesz basic sequences.
Conjectureopenfunctional-analysis kadison-singer riesz-sequencesarXiv posted 2 days ago
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The finite-union conjecture for bounded below approximate Schauder frames
Finite-union conjecture. Every bounded below ASF can be partitioned as a finite union of ARSs. The source's statement uses “ARBs,” but the preceding definition introduces ARSs; thi…
Conjectureopenbanach-spaces frame-theory riesz-sequencesarXiv posted 2 days ago

The quantitative RϵR_\epsilonRϵ​-conjecture for finite Riesz basic sequences