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Algebras of operators in Banach spaces over the quaternion skew field and the octonion algebras

S. V. Ludkovsky
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Abstract

The article is devoted to quasilinear operators in spaces over quaternions and octonions. Spectral theory of bounded and unbounded operators is investigated. Analogs of C^* algebras are defined and studied. Among main results are analogs of the Gelfand-Mazur, Stone, Gelfand-Naimark-Segal, von Neumann, Kaplansky, etc. theorems, but here over the skew field of quaternions and the octonion algebra.

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S. V. Ludkovsky. 2006-03-01. Algebras of operators in Banach spaces over the quaternion skew field and the octonion algebras. https://arxiv.org/abs/math/0603025

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