On bilinear forms from the point of view of generalized effect algebras. (English) Zbl 1285.81003

The authors show that various families of positive bilinear forms on a Hilbert space might be organized as a generalized effect algebra and clarify which of considered subfamilies are substructures. Moreover, they study monotone Dedekind downwards and upwards \(\sigma\)-completeness of these effect algebras and present an example that we can obtain another result if we use the usual partial order of positive bilinear forms instead of that induced by the generalized effect algebra structure.


81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03G25 Other algebras related to logic
03G12 Quantum logic
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