Inner automorphisms of hyperfinite factors and Bogoliubov transformations
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...
Let ℳ be a von Neumann factor of type II1 with a normalized trace τ. In 1983 L. G. Brown showed that to every operator T∈ℳ one can in a natural way associate a spectral distribution measure μ T (now called the Brown measure of T), which is a probability measure in ℂ with support in the spectrum σ(T) of T. In this paper it is shown that for every T∈ℳ and every Borel set B in ℂ, there is a unique closed T-invariant subspace affiliated with ℳ, such that the Brown measure of is concentrated on B...