Abstract
The quantum effects for a physical system can be described by the set of positive operators on a complex Hilbert space that are bounded above by the identity operator . For , let be the sequential product and let be the Jordan product of . The main purpose of this note is to study some of the algebraic properties of effects. Many of our results show that algebraic conditions on and imply that and have diagonal operator matrix forms with as an orthogonal projection on closed subspace being the common part of and . Moreover, some generalizations of results known in the literature and a number of new results for bounded operators are derived.
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