Consider the linear general eigenvalue problem Ay = λBy , where A and B are both invertible and Hermitian N × N matrices. In this paper we construct a set of meromorphic functions, the Krein eigenvalues, whose zeros correspond to the real eigenvalues of the general eigenvalue problem. The Krein eigenvalues are generated by the Krein matrix, which is constructed through projections on the positi...

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 ...

We construct rather general random ensembles that yield the optimal (isomorphic) estimate in Dvoretzky-Milman Theorem. This is first construction of non gaussian/spherical exhibit behaviour. The constructed here need not satisfy any rotation invariance and can be heavy-tailed.

The basic higher order commutator theorem is formulated for the real interpolation methods associated with the quasi-power parameters, that is, the function spaces on which Hardy inequalities are valid. This theorem unifies and extends various results given by Cwikel, Jawerth, Milman, Rochberg, and others, and incorporates some results of Kalton to the context of commutator estimates for the re...

This paper is about the structure of all entrance laws (in sense Dynkin) for time-inhomogeneous Ornstein–Uhlenbeck processes with Lévy noise in Hilbert state spaces. We identify extremal finite weak first moments through an explicit formula their Fourier transforms, generalizing corresponding results by Dynkin Wiener and nuclear then prove that arbitrary law can be uniquely represented as integ...