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arXiv · 2309.10297

Approximate ultrahomogeneity in $L_pL_q$ lattices

Mary Angelica Tursi
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Abstract

We show that for $1\leq p, q<\infty$ with $p/q \notin \mathbb{N}$, the doubly atomless separable $L_pL_q$ Banach lattice $L_p(L_q)$ is approximately ultrahomogeneous (AUH) over the class of its finitely generated sublattices. The above is not true when $p/q \in \mathbb{N}$. However, for any $p\neq q$, $L_p(L_q)$ is AUH over the finitely generated lattices in the class $BL_pL_q$ of bands of $L_pL_q$ lattices.

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Mary Angelica Tursi. 2023-09-19. Approximate ultrahomogeneity in $L_pL_q$ lattices. https://arxiv.org/abs/2309.10297

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