This paper generalizes polyhedra to infinite dimensional separable Hilbert spaces as countable intersections of closed semispaces. We show that a polyhedron is the sum of convex proper subset, which is compact in the product topology, plus a closed pointed cone plus a closed subspace. In the final part the dual range space technique is extended to solve infinite dimensional LP problems.

The Kadison-Kastler problem asks whether close C*-algebras on a Hilbert space must be spatially isomorphic. We establish this when one of the algebras is separable and nuclear. We also apply our methods to the study of near inclusions of C*-algebras.

In this article, we study a class of impulsive stochastic neutral partial functional differential equations in a real separable Hilbert space. By using Banach fixed point theorem, we give sufficient conditions for the existence and uniqueness of a mild solution. Also the exponential p-stability of a mild solution and its sample paths are obtained.

We de ne and characterize a frame-like stable decomposition for subspaces of a general separable Hilbert space. We call it pseudoframes for subspaces (PFFS). Properties of PFFS are discussed. A necessary and su cient characterization of PFFSs is provided. Analytical formulae for the construction of PFFSs are derived. Examples and applications of PFFSs are discussed.

Given two self-adjoint, positive, compact operators A,B on a separable Hilbert space, we show that there exists a self-adjoint, positive, compact operator C commuting with B such that limt→∞ ||(e Bt 2 ee Bt 2 ) 1 t − e || = 0. 1

The aim of this paper is to show that the automorphism and isometry groups of the suspension of B(H), H being a separable infinite dimensional Hilbert space, are algebraically reflexive. This means that every local automorphism, respectively local surjective isometry of C0(R) ⊗ B(H) is an automorphism, respectively a surjective isometry.

If X is a Banach space such that the isomorphism constant to `2 from n dimensional subspaces grows sufficiently slowly as n → ∞, then X has the approximation property. A consequence of this is that there is a Banach space X with a symmetric basis but not isomorphic to `2 so that all subspaces of X have the approximation property. This answers a problem raised in 1980 [8]. An application of the ...

Let A and B be separable nuclear continuous C(X)-algebras over a finite dimensional compact metrizable space X. It is shown that an element σ of the parametrized Kasparov group KKX(A,B) is invertible if and only all its fiberwise components σx ∈ KK(A(x), B(x)) are invertible. This criterion does not extend to infinite dimensional spaces since there exist nontrivial unital separable continuous f...

We discuss some nonlinear problems associated with an infinite dimensional operator L defined on a real separable Hilbert space H. As the operator L we choose the Ornstein-Uhlenbeck operator induced by a centered Gaussian measure μ with covariance operator Q.

In this paper we calibrate the stationary Gaussian Musiela model to time series of market data using the Karhunen-Loeve expansion in order to get an ortonormal basis (classically known as EOF, empirical orthonormal functions) in a separable Hilbert space. The basis found is optimal for representing the covariance of the invariant measure of the forward rates’ process.