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arXiv · 2509.08796

Strictly singular operators on the Baernstein and Schreier spaces

Niels Jakob Laustsen·JamesSmith
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Abstract

Every composition of two strictly singular operators is compact on the Baernstein space $B_p$ for $1 < p < \infty$ and on the $p$-convexified Schreier space $S_{p}$ for $1 \leq p < \infty$. Furthermore, every subsymmetric basic sequence in $B_p$ (respectively, $S_p$) is equivalent to the unit vector basis for $\ell_p$ (respectively, $c_0$), and the Banach spaces $B_p$ and $S_p$ contain block basic sequences whose closed span is not complemented.

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Niels Jakob Laustsen, JamesSmith. 2025-09-10. Strictly singular operators on the Baernstein and Schreier spaces. https://arxiv.org/abs/2509.08796

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