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arXiv · 2506.07487

Extendable Shift Maps and Weighted Endomorphisms on Generalized Countable Markov Shifts

Rodrigo Bissacot·Iván Diaz-Granados·Thiago Raszeja
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Abstract

We obtain an operator algebraic characterization for when we can continuously extend the shift map from a standard countable Markov shift $\Sigma_A$ to its respective generalized countable Markov shift $X_A$ (a compactification of $\Sigma_A$). When the shift map is continuously extendable, we obtain explicit formulas for the spectral radius of weighted endomorphisms $a\alpha$, where $\alpha$ is dual to the shift map and conjugated to $\Theta(f)=f \circ \sigma$ on $C(X_A)$, extending a theorem of Kwa\'sniewski and Lebedev from finite to countable alphabets.

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Rodrigo Bissacot, Iván Diaz-Granados, Thiago Raszeja. 2025-06-09. Extendable Shift Maps and Weighted Endomorphisms on Generalized Countable Markov Shifts. https://arxiv.org/abs/2506.07487

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