Weakly Ordered A-Commutative Partial Groups of Linear Operators Densely Defined on Hilbert Space
Keyword(s):
The notion of a generalized effect algebra is presented as a generalization of effect algebra for an algebraic description of the structure of the set of all positive linear operators densely defined on a Hilbert space with the usual sum of operators. The structure of the set of not only positive linear operators can be described with the notion of a weakly ordered partial commutative group (wop-group).Due to the non-constructive algebraic nature of the wop-group we introduce its stronger version called a weakly ordered partial a-commutative group (woa-group). We show that it also describes the structure of not only positive linear operators.
2011 ◽
Vol 50
(1)
◽
pp. 63-78
Keyword(s):
1987 ◽
Vol 39
(4)
◽
pp. 880-892
◽
1984 ◽
Vol 97
◽
pp. 79-95
◽
2011 ◽
Vol 68
(3)
◽
pp. 261-270
◽
Keyword(s):
1984 ◽
Vol 27
(2)
◽
pp. 229-233
◽
1994 ◽
Vol 17
(1)
◽
pp. 27-30
2010 ◽
Vol 47
(3)
◽
pp. 289-298
◽