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The main purpose of this paper is to investigate some natural problems regarding the order structure of representable functionals on *-algebras. We describe the extreme points of order intervals, and give a non-trivial sufficient condition to decide whether or not the infimum of two representable functionals exists. To this aim, we offer a suitable approach to the Lebesgue decomposition theory, which is in complete analogy with the one developed by Ando in the context of positive operators. This tight analogy allows to invoke Ando's results to characterize uniqueness of the decomposition, and solve the infimum problem over certain operator algebras.



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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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