Inequalities in Von Neumann Algebras
The paper gives new integral representations of the -Drazin inverse of an element of a -algebra that require no restriction on the spectrum of . The representations involve powers of and of its adjoint.
We present a way of thinking of exponential farnilies as geodesic surfaces in the class of positive functions considered as a (multiplicative) sub-group G+ of the group G of all invertible elements in the algebra A of all complex bounded functions defined on a measurable space. For that we have to study a natural geometry on that algebra. The class D of densities with respect to a given rneasure will happen to be representatives of equivalence classes defining a projective space in A. The natural...