Weakly ordered partial commutative group of self-adjoint linear operators densely defined on Hilbert space

Janda, Jiří

doi:10.2478/v10127-011-0037-x

Abstract

We continue in a direction of describing an algebraic structure of linear operators on infinite-dimensional complex Hilbert space ℋ. In [Paseka, J.- -Janda, J.: More on PT-symmetry in (generalized) effect algebras and partial groups, Acta Polytech. 51 (2011), 65-72] there is introduced the notion of a weakly ordered partial commutative group and showed that linear operators on H with restricted addition possess this structure. In our work, we are investigating the set of self-adjoint linear operators on H showing that with more restricted addition it also has the structure of a weakly ordered partial commutative group.

References

[1] BLANK, J.-EXNER, P.-HAVLÍČEK,M.: Hilbert Space Operators in Quantum Physics (2nd ed.), Springer-Verlag, Berlin, 2008.
Search in Google Scholar
[2] HEDLÍKOVÁ, J.-PULMANNOVÁ, S.: Generalized difference posets and orthoalgebras, Acta Math. Univ. Comenianae 45 (1996), 247-279.
Search in Google Scholar
[3] DVUREČENSKIJ, A.-PULMANNOVÁ, S.: New Trends in Quantum Structures. Kluwer Acad. Publ., Dordrecht/Ister Science, Bratislava, 2000.10.1007/978-94-017-2422-7
Search in Google Scholar
[4] FOULIS, D. J.-BENNETT, M. K.: Effect algebras and unsharp quantum logics, Found. Phys. 24 (1994), 1331-1352.10.1007/BF02283036
Search in Google Scholar
[5] PASEKA, J.: PT -symmetry in (generalized) effect algebras, Internat. J. Theoret. Phys. 50 (2011), 1198-1205.10.1007/s10773-010-0594-9
Search in Google Scholar
[6] PASEKA, J.-JANDA, J.: More on PT -symmetry in (generalized) effect algebras and partial groups, Acta Polytech. 51 (2011), 65-72.10.14311/1408
Search in Google Scholar
[7] PASEKA, J.-RIEČANOVÁ, Z.: Considerable sets of linear operators in Hilbert spaces as generalized effect algebras. Found. Phys. 41 (2011), 1634-1647.
Search in Google Scholar
[8] POLAKOVIĆ, M.-RIEĆANOVÁ , Z.: Generalized effect algebras of positive operators densely defined on Hilbert spaces, Internat. J. Theoret. Phys. 50 (2011), 1167-1174.10.1007/s10773-010-0458-3
Search in Google Scholar
[9] RIEĆANOVÁ, Z.-ZAJAC, M.-PULMANNOVÁ, S.: Effect algebras of positive opera- tors densely defined on Hilbert spaces, Rep. Math. Phys., 2011 (accepted).10.1016/S0034-4877(12)60009-3
Search in Google Scholar
[10] RIEĆANOVÁ, Z.: Effect algebras of positive self-adjoint operators densely defined on Hilbert spaces, Acta Polytech. 51 (2011), 78-82.
Search in Google Scholar
[11] RIEĆANOVÁ, Z.-ZAJAC, M.: Extensions of effect algebra operations, Acta Polytech. 51 (2011), 73-77.
Search in Google Scholar

Weakly ordered partial commutative group of self-adjoint linear operators densely defined on Hilbert space

Abstract

Paradigm

My account