Spectral resolution in a Rickart comgroup |
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Authors: | David J Foulis |
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Institution: | Emeritus Professor, University of Massachusetts; 1 Sutton Court, Amherst, MA 01002, USA |
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Abstract: | A comgroup is a compressible group with the general comparability property. A comgroupwith the Rickart projection property is called a Rickart comgroup. We show that each element of a Rickart comgroup has a rational spectral resolution and a nonempty closed and bounded (real) spectrum. The rational spectral resolution and the spectrum are shown to have many of the properties of the spectral resolution and spectrum of a self-adjoint operator on a Hilbert space. Examples of Rickart comgroups include the additive group of self-adjoint elements in a von Neumann algebra and the Mundici group of a Heyting MV algebra. |
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Keywords: | Partially ordered abelian group compressible group projection general comparability comgroup Rickart projection property rational spectral resolution eigenvalue spectrum |
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