We study refinements between spectral resolutions in an arbitrary II1 factor M and obtain diffuse (maximal) refinements of spectral resolutions. We construct models of operators with respect to diffuse spectral resolutions. ...

Let A be a C*-algebra and φ{symbol} : A → L (H) be a positive unital map. Then, for a convex function f : I → R defined on some open interval and a self-adjoint element a ∈ A whose spectrum lies in I, we obtain a Jensen's-type ...