Spectral Theory of Almost Periodic Banach--Malcev Algebras and Applications to Moufang Dynamics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917146492141568 |
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| author | Ennaceur, Marwa |
| author_facet | Ennaceur, Marwa |
| contents | We introduce almost periodic Banach--Malcev algebras as a non-associative extension of Bohr's classical theory. Our framework is based on the relative compactness of adjoint orbits $\{e^{t\,\mathrm{ad}(x)}(y)\}$, which yields the spectral characterization $σ(\mathrm{ad}(x)) \subseteq i\mathbb{R}$, uniform boundedness of orbit closures in the strong operator topology, and a continuous functional calculus for almost periodic derivations. Compact Malcev algebras -- most notably the imaginary octonions $\mathrm{Im}(\mathbb{O})$ -- provide canonical finite-dimensional examples, and their associated Moufang loops carry strictly periodic flows. We also analyze structural actions on eigenspaces of the Malcev Laplacian as a concrete case study, where the bounded defect operator $S(x,y) \in \mathcal{B}(M)$ quantifies the non-associative correction. While speculative links to non-associative gauge theory are noted, they lie beyond the established mathematical scope. The recent convergence control of the BCH series for special Banach--Malcev algebras \cite{Athmouni2025} provides analytic justification for the local Moufang structure used throughout. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12687 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral Theory of Almost Periodic Banach--Malcev Algebras and Applications to Moufang Dynamics Ennaceur, Marwa Differential Geometry Mathematical Physics Functional Analysis 46H70, 47D03, 43A60, 17D10, 53C30 G.1.3; F.2.1; I.1.2 We introduce almost periodic Banach--Malcev algebras as a non-associative extension of Bohr's classical theory. Our framework is based on the relative compactness of adjoint orbits $\{e^{t\,\mathrm{ad}(x)}(y)\}$, which yields the spectral characterization $σ(\mathrm{ad}(x)) \subseteq i\mathbb{R}$, uniform boundedness of orbit closures in the strong operator topology, and a continuous functional calculus for almost periodic derivations. Compact Malcev algebras -- most notably the imaginary octonions $\mathrm{Im}(\mathbb{O})$ -- provide canonical finite-dimensional examples, and their associated Moufang loops carry strictly periodic flows. We also analyze structural actions on eigenspaces of the Malcev Laplacian as a concrete case study, where the bounded defect operator $S(x,y) \in \mathcal{B}(M)$ quantifies the non-associative correction. While speculative links to non-associative gauge theory are noted, they lie beyond the established mathematical scope. The recent convergence control of the BCH series for special Banach--Malcev algebras \cite{Athmouni2025} provides analytic justification for the local Moufang structure used throughout. |
| title | Spectral Theory of Almost Periodic Banach--Malcev Algebras and Applications to Moufang Dynamics |
| topic | Differential Geometry Mathematical Physics Functional Analysis 46H70, 47D03, 43A60, 17D10, 53C30 G.1.3; F.2.1; I.1.2 |
| url | https://arxiv.org/abs/2512.12687 |