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Considerable sets of linear operators in Hilbert spaces as operator generalized effect algebras. (English) Zbl 1238.81009
The authors study numerous families of positive linear operators on Hilbert spaces and show that these form (generalized) effect algebras. In these cases, when the partial effect-algebraic sum is defined, it coincides with the ordinary sum of operators. The possibility of extension of this partial operation to unbounded operators is discussed and related open problems are formulated.

MSC:
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06C15 Complemented lattices, orthocomplemented lattices and posets
47B65 Positive linear operators and order-bounded operators
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