Algebras of operators in Banach spaces over the quaternion skew field   and the octonion algebras
  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. 
S. V. Ludkovsky