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Orthomodular spaces are the counterpart of Hilbert spaces for fields other than or . Both share numerous properties, foremost among them is the validity of the Projection theorem. Nevertheless in the study of bounded linear operators which started in [], there appeared striking differences with the classical theory. In fact, in this paper we shall construct, on the canonical non-archimedean orthomodular space of [], two infinite families of self-adjoint bounded linear operators having no invariant...
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