The authors establish left and right slice regular functional calculi for power-associative operators over octonions using pull-back and push-forward spectra, unifying the theory across complex, quaternion, and octonion algebras.
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Para-linear isometric isomorphisms on octonionic Hilbert bimodules are equivalent to mapping associative orthonormal bases to weak associative orthonormal bases, extending to partial isometries and a new perspective on James questions.
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Octonionic Riesz-Dunford functional calculus
The authors establish left and right slice regular functional calculi for power-associative operators over octonions using pull-back and push-forward spectra, unifying the theory across complex, quaternion, and octonion algebras.
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Octonionic isometric isomorphisms and partial isometry
Para-linear isometric isomorphisms on octonionic Hilbert bimodules are equivalent to mapping associative orthonormal bases to weak associative orthonormal bases, extending to partial isometries and a new perspective on James questions.