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

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