Effect Algebras of Positive Self-adjoint Operators Densely Defined on Hilbert Spaces

Z. Riečanová

Abstract


We show that (generalized) effect algebras may be suitable very simple and natural algebraic structures for sets of (unbounded) positive self-adjoint linear operators densely defined on an infinite-dimensional complex Hilbert space. In these cases the effect algebraic operation, as a total or partially defined binary operation, coincides with the usual addition of operators in Hilbert spaces.

Keywords


quantum structures; (generalized) effect algebra; Hilbert space; (unbounded) positive linear operator

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague