Abstract
Let C be the complex Levi-Civita field and let c 0(C) or, simply, c 0 denote the space of all null sequences of elements of C. A non-Archimedean norm is defined naturally on c 0 with respect to which c 0 is a Banach space. In this paper, we study the properties of positive operators on c 0 which are similar to those of positive operators in classical functional analysis; however the proofs of many of the results are nonclassical. Then we use our study of positive operators to introduce a partial order on the set of compact and self-adjoint operators on c 0 and study the properties of that partial order.
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