Considerable Sets of Linear Operators in Hilbert Spaces as Operator Generalized Effect Algebras

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Authors	PASEKA Jan RIEČANOVÁ Zdenka
Year of publication	2011
Type	Article in Periodical
Magazine / Source	Foundations of Physics
MU Faculty or unit	Faculty of Science
Citation
Web	http://www.springerlink.com/content/34h7p0018736878x/
Doi	http://dx.doi.org/10.1007/s10701-011-9573-0
Field	General mathematics
Keywords	Quantum structures; (Generalized) effect algebra; Hilbert space; (Unbounded) positive linear operator; Closure; Adjoint; Friedrichs extension
Description	We show that considerable sets of positive linear operators namely their extensions as closures, adjoints or Friedrichs positive self-adjoint extensions form operator (generalized) effect algebras. Moreover, in these cases the partial effect algebraic operation of two operators coincides with usual sum of operators in complex Hilbert spaces whenever it is defined. These sets include also unbounded operators which play important role of observables (e.g., momentum and position) in the mathematical formulation of quantum mechanics.
Related projects:	Mathematical structures and their physical applications