On the Structure of Generalized Effect Algebras and Separation Algebras

2018 ◽  
pp. 148-165
Author(s):  
Sarah Alexander ◽  
Peter Jipsen ◽  
Nadiya Upegui
Keyword(s):  
Effect Algebras ◽  
Generalized Effect Algebras

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

2011 ◽  
Vol 50 (1) ◽  
pp. 63-78
Author(s):  
Jiří Janda
Keyword(s):  
Hilbert Space ◽  
Algebraic Structure ◽  
Complex Hilbert Space ◽  
Commutative Group ◽  
Pt Symmetry ◽  
Linear Operators ◽  
Effect Algebras ◽  
Infinite Dimensional ◽  
Densely Defined ◽  
Generalized Effect Algebras

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.

Topological Properties of Operator Generalized Effect Algebras

2012 ◽  
Vol 69 (3) ◽  
pp. 311-320 ◽  
Author(s):  
S. Pulmannová ◽  
Z. Riečanová ◽  
M. Zajac
Keyword(s):  
Effect Algebras ◽  
Topological Properties ◽  
Generalized Effect Algebras

Riesz ideals in generalized effect algebras and in their unitizations

2007 ◽  
Vol 57 (4) ◽  
pp. 393-417 ◽  
Author(s):  
S. Pulmannová ◽  
E. Vinceková
Keyword(s):  
Effect Algebras ◽  
Generalized Effect Algebras

Blocks in Pairwise Summable Generalized Effect Algebras

2014 ◽  
Vol 73 (2) ◽  
pp. 213-223
Author(s):  
Zdenka Riečanová ◽  
Jiří Janda ◽  
Wu Junde
Keyword(s):  
Effect Algebras ◽  
Generalized Effect Algebras

scholarly journals Regular Gleason Measures and Generalized Effect Algebras

2015 ◽  
Vol 54 (12) ◽  
pp. 4313-4326
Author(s):  
Anatolij Dvurečenskij ◽  
Jiří Janda
Keyword(s):  
Effect Algebras ◽  
Generalized Effect Algebras

scholarly journals Intervals in Generalized Effect Algebras and their Sub-generalized Effect Algebras

10.14311/1817 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Zdenka Riečanová ◽  
Michal Zajac
Keyword(s):  
Effect Algebra ◽  
Effect Algebras ◽  
Generalized Effect Algebra ◽  
Generalized Effect Algebras

We consider subsets G of a generalized effect algebra E with 0∈G and such that every interval [0, q]G = [0, q]E ∩ G of G (q ∈ G , q ≠ 0) is a sub-effect algebra of the effect algebra [0, q]E. We give a condition on E and G under which every such G is a sub-generalized effect algebra of E.

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