Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1901050 | Reports on Mathematical Physics | 2012 | 8 Pages |
Abstract
In answer to open questions (posed in [12]) we prove that an effect algebra has a Hilbert space effect-representation iff E possesses an ordering set of states. These are, up to isomorphism, all intervals and all their sub-effect algebras in the set of all positive linear operators on any Hilbert space HH. Nevertheless, there are effect algebras E, elements of which are linear operators in a Hilbert space, but E does not have such a representation.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Z. Riečanová, M. Zajac,