Abstract:We classify the distributional self-embeddings of the centered first limit Bourgain-Rosenthal-Schechtman space $R_\omega^{p,0}$, $1<p<\infty$. Using a Boolean rigidity principle for its canonical independent-sum realization, we show that every such embedding is induced by a finite packing of Bernoulli factors. As a consequence, we also prove that $R_\omega^{p,0}$ admits no proper non-zero internal compressions. Moreover, for $p\notin2\mathbb N$, we obtain a complete description of the linear isometric embeddings of the non-centered space $R_\omega^p$, and, for $p\neq2$, we determine its group of surjective linear isometries.
From: Juan Carlos Sampedro [view email]
[v1]
Tue, 9 Jun 2026 00:01:16 UTC (17 KB)
[v2]
Wed, 17 Jun 2026 15:07:55 UTC (24 KB)
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