1206.2751 (Anatoly N. Kochubei)
Anatoly N. Kochubei
The spectral theorem proved recently for a class of bounded linear operators on non-Archimedean Banach spaces (A. N. Kochubei, Non-Archimedean normal operators, J. Math. Phys. 51 (2010), article 023526) opens the way to developing a theory of non-Archimedean operator algebras. We present first results in this direction, with an emphasis on the new objects, often far from their classical counterparts, and new problems. In particular, we consider some algebras containing non-Archimedean normal operators, algebras whose residue field reductions are Baer rings, and a non-Archimedean version of the crossed product construction.
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http://arxiv.org/abs/1206.2751
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