Non-Archimedean Operator Algebras
We consider some classes of algebras of bounded linear operators on Banach spaces over non-Archimedean fields. In particular, we propose a possible way based on the notion of a Baer ring  to introduce a non-Archimedean version of the notion of a von Neumann algebra. Two methods of constructing examples of such algebras are given. We develop an analog of the crossed product construction, one of the main methods of constructing von Neumann algebras in the classical case. This results  in a class of non-trivial non-Archimedean factors (algebras with a trivial center) or algebras close to factors corresponding, through the reduction procedure, to type I Baer rings. In the second construction, the algebras are generated by regular representations of discrete groups. In this situation , algebras of types I and III are obtained.
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