Composition operators Cφ on the Hilbert Hardy space H 2 over the unit disk are considered. We investigate when convergence of sequences {φn} of symbols, (i.e., of analytic selfmaps of the unit disk) towards a given symbol φ, implies the convergence of the induced composition operators, Cφn → Cφ . If the composition operators Cφn are Hilbert–Schmidt operators, we prove that convergence in the Hi...

We consider a conformal field theory for bosons on the Riemann sphere. Correlation functions are defined as singular limits of functional integrals. The main result is that these amplitudes define transition amplitudes, that is multilinear Hilbert-Schmidt functionals on a fixed Hilbert space.

This paper deals with bracket flows of Hilbert-Schmidt operators. We establish elementary convergence results for such flows and discuss some of their consequences.

Current work defines Schmidt representation of a bilinear operator T:H1×H2→K, where H1,H2 and K are separable Hilbert spaces. Introducing the concept singular value ordered value, we prove that if T is compact, its values ordered, then has on real We hypothesis existence fundamental.

This work presents a parametrized family of distances, namely the Alpha Procrustes on set symmetric, positive definite (SPD) matrices. The distances provide unified formulation encompassing both Bures-Wasserstein and Log-Euclidean between SPD We show that are Riemannian corresponding to metrics manifold matrices, which encompass Wasserstein metrics. is then generalized Hilbert-Schmidt operators...