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Self-improvement for absolutely Cesáro bounded operators
We prove that every $p$-absolutely Cesàro bounded operator with constant $K>1$ is $q$-absolutely Cesàro bounded for $1\leq q<pK/(K-1)$. This range is optimal, even for positive weighted shifts. On Banach spaces of type $s\in (1,2]$, we prove that every absolutely Cesàro bounded operator is $q$-absol
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