Any Regular Measure on Conjugation Logic is a Complex Measure

Abstract

Let H be the complex Hilbert space with conjugation J. Denote by B(H)co the quantum logic of all J-projections on H. A non-zero function μ({dot operator}):=tr(A({dot operator})) on B(H)co is said to be a regular measure. Here A is a trace class operator. It is shown that there exists a J-projection p such that. We give a description of the hermitian and skew hermitian regular measures. © 2011 Springer Science+Business Media, LLC.