Gorde:
| Egile Nagusiak: | , |
|---|---|
| Formatua: | Preprint |
| Argitaratua: |
2025
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| Gaiak: | |
| Sarrera elektronikoa: | https://arxiv.org/abs/2509.02405 |
| Etiketak: |
Etiketa erantsi
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Aurkibidea:
- Let $X$ be the direct sum of finitely many Banach spaces chosen from the following three families: (i) the Baernstein spaces $B_p$ for $1<p<\infty$; (ii) the $p$-convexified Schreier spaces $S_p$ for $1\le p<\infty$; (iii) the sequence spaces $\ell_p$ for $1\le p<\infty$ (and $c_0$). We show that the quotient algebra of strictly singular by compact operators on $X$ is nilpotent; that is, there is a natural number $k$, dependent only on the collections of direct summands from each of the three families, such that: - every composition of $k+1$ strictly singular operators on $X$ is compact; - there are $k$ strictly singular operators on $X$ whose composition is not compact.