Trace class operators Cont Last time I define and operator to be of 'trace class' if it is a finite sum of products of Hilbert-Schmidt operators (1) T =

The Brockett-Wegner diagonalizing flow Ḣt = [ Ht, [Ht, A] ] is studied. Global existence and uniqueness of solutions of this evolution equation is proved on the space B[H ] of bounded operators on a complex Hilbert space H . Local existence is proved for certain unbounded initial operators H0. Furthermore, if H0, A are Hilbert-Schmidt operators, it is demonstrated that Ht strongly converges to ...

Many machine learning algorithms can be formulated in the framework of statistical independence such as the Hilbert Schmidt Independence Criterion. In this paper, we extend this criterion to deal with structured and interdependent observations. This is achieved by modeling the structures using undirected graphical models and comparing the Hilbert space embeddings of distributions. We apply this...

We introduce a Riemannian metric with non positive curvature in the (infinite dimensional) manifold Σ∞ of positive invertible operators of a Hilbert space H, which are scalar perturbations of Hilbert-Schmidt operators. The (minimal) geodesics and the geodesic distance are computed. It is shown that this metric, which is complete, generalizes the well known non positive metric for positive defin...