Extendable Shift Maps and Weighted Endomorphisms on Generalized Countable Markov Shifts
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910995744555008 |
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| author | Bissacot, Rodrigo Diaz-Granados, Iván Raszeja, Thiago |
| author_facet | Bissacot, Rodrigo Diaz-Granados, Iván Raszeja, Thiago |
| contents | We obtain an operator algebraic characterization for when we can continuously extend the shift map from a standard countable Markov shift $Σ_A$ to its respective generalized countable Markov shift $X_A$ (a compactification of $Σ_A$). When the shift map is continuously extendable, we obtain explicit formulas for the spectral radius of weighted endomorphisms $aα$, where $α$ is dual to the shift map and conjugated to $Θ(f)=f \circ σ$ on $C(X_A)$, extending a theorem of Kwaśniewski and Lebedev from finite to countable alphabets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07487 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extendable Shift Maps and Weighted Endomorphisms on Generalized Countable Markov Shifts Bissacot, Rodrigo Diaz-Granados, Iván Raszeja, Thiago Dynamical Systems Functional Analysis Operator Algebras 37B10, 81Q10, 37D35, 37C30, 28Dxx, 46Lxx, 37A55, 46L55, 47B93, 46Jxx, 46J10 We obtain an operator algebraic characterization for when we can continuously extend the shift map from a standard countable Markov shift $Σ_A$ to its respective generalized countable Markov shift $X_A$ (a compactification of $Σ_A$). When the shift map is continuously extendable, we obtain explicit formulas for the spectral radius of weighted endomorphisms $aα$, where $α$ is dual to the shift map and conjugated to $Θ(f)=f \circ σ$ on $C(X_A)$, extending a theorem of Kwaśniewski and Lebedev from finite to countable alphabets. |
| title | Extendable Shift Maps and Weighted Endomorphisms on Generalized Countable Markov Shifts |
| topic | Dynamical Systems Functional Analysis Operator Algebras 37B10, 81Q10, 37D35, 37C30, 28Dxx, 46Lxx, 37A55, 46L55, 47B93, 46Jxx, 46J10 |
| url | https://arxiv.org/abs/2506.07487 |