Abstract
Orthomodular spaces are generalizations ofHilbert spaces with which they share the basic propertyexpressed by the Projection Theorem. We study twoinfinite-dimensional orthomodular spaces, bothconstructed over the same field of power series, but withdifferent inner products. On the first space everybounded, self-adjoint operator decomposes into anorthogonal sum of operators of rank 1 or 2; on thesecond space, in contrast, there exist self-adjointoperators that are undecomposable. These differencesreflect the fact that the underlying geometries aredissimiliar.
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Keller, H.A., Herminia, O.A. On the Geometry of Orthomodular Spaces over Fields of Power Series. International Journal of Theoretical Physics 37, 85–92 (1998). https://doi.org/10.1023/A:1026613222627
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DOI: https://doi.org/10.1023/A:1026613222627