ABSTRACT
Suppose A https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137292/676aa42d-79c8-4246-bc0f-e0fd47650f7d/content/eq943.tif"/> is a C*-algebra and φ is a linear functional on A.
We say that φ is Hermitian if φ ( x * ) = φ ( x ) ¯ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137292/676aa42d-79c8-4246-bc0f-e0fd47650f7d/content/eq944.tif"/> for all x ∈ A https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137292/676aa42d-79c8-4246-bc0f-e0fd47650f7d/content/eq945.tif"/> .
We say that φ is positive if φ(x) ≥ 0 for all x ≥ 0.
We say that φ is a state if φ is positive and φ(1) = 1.
