<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

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

Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, CZ–611-37 Brno, CZECH REPUBLIC

Tatra Mountains Mathematical Publications

We continue in a direction of describing an algebraic structure of linear operators on infinite-dimensional complex Hilbert space ℋ. In [Paseka, J.- -Janda,...

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

Published Online: Nov 13, 2012

Page range: 63 - 78

DOI: https://doi.org/10.2478/v10127-011-0037-x

This content is open access.