We revisit the Krein-von Neumann extension in case where underlying symmetric operator is strictly positive and apply this to derive explicit form of for singular, general (i.e., three-coefficient) Sturm-Liouville operators on arbitrary intervals. In particular, boundary conditions minimal are explicitly expressed terms generalized values adapted (possible) singularity structure coefficients ne...

Our aim in this paper is to make explicit the operator theory of the heuristic open Bosonic string and to abstract a suitable field algebra for the string. This is done on a Fock-Krein space and we examine integrability and J-unitary implementability of all the defining transformations of the string, i.e. time translations, gauge transformations and Poincare transformations. The results obtaine...

This paper describes how one can use the well-known Bayesian prior to posterior analysis of the Dirichlet process, and less known results for the gamma process, to address the formidable problem of assessing the distribution of linear functionals of Dirichlet processes. In particular, in conjunction with a gamma identity, we show easily that a generalized Cauchy-Stieltjes transform of a linear ...

Let G be an antipodal distance regular cover of a complete graph with index T'. If T' = 2 then it is known that the neighbourhood of a vertex in G is strongly regular, and the Krein bound is tight for G. We use the theory of spherical designs ( due to Delsarte, Goethals and Seidel) to show that if r > 2 and the Krein bound is tight for G then the neighbourhood of any vertex in G is strongly reg...

M. Krein proved in [KR48] that if T is a continuous operator on a normed space leaving invariant an open cone, then its adjoint T ∗ has an eigenvector. We present generalizations of this result as well as some applications to C∗-algebras, operators on l1, operators with invariant sets, contractions on Banach lattices, the Invariant Subspace Problem, and von Neumann algebras. M. Krein proved in ...