In this paper we present a brief review of some important results on weak compactness in the space of vector valued measures. We also review some recent results of the author on weak compactness of any set of operator valued measures. These results are then applied to optimal structural feedback control for deterministic systems on infinite dimensional spaces.

Let V be a system of weights on a completely regular Hausdorff space and let B(E) be the topological vector space of all continuous linear operators on a Hausdorff topological vector space E. Let CV0(X,E) and CVb(X,E) be the nonlocally convex weighted spaces of continuous functions. In the present paper, we characterize compact multiplication operators Mψ on CV0 (X,E) ( or CVb(X,E)) induced by ...

We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends to higher multiplicity their dilation approach. We prove several results for operator-valued frames concerning duality, disjointeness, complementar...

Let {X1, . . . ,Xp} be complex-valued vector fields in Rn and assume that they satisfy the bracket condition (i.e. that their Lie algebra spans all vector fields). Our object is to study the operator E = ∑ X∗ i Xi, where X ∗ i is the L2 adjoint of Xi. A result of Hörmander is that when the Xi are real then E is hypoelliptic and furthemore it is subelliptic (the restriction of a destribution u t...

This work concerns the approximation of the shape operator of smooth surfaces in R from polyhedral surfaces. We introduce two generalized shape operators that are vector-valued linear functionals on a Sobolev space of vector fields and can be rigorously defined on smooth and on polyhedral surfaces. We consider polyhedral surfaces that approximate smooth surfaces and prove two types of approxima...

In this paper, we introduce the idea of generalized Ritt type and generalised Ritt weak type of entire functions represented by a vector valued Dirichlet series. Hence, we study some growth properties of two entire functions represented by a vector valued Dirichlet series on the basis of generalized Ritt type and generalised Ritt weak type.

The Maurey-Rosenthal theorem states that each bounded and linear operator T from a quasi normed space E into some L p (ν) (0 < p < r < ∞) which satisfies a vector-valued norm inequality

First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit infinite (but still incomplete) sets of exact (algebraic) solutions. The hamiltonians of these models are hermitian operators of the form H = −∆ +V1(r)+ (s · l)V2(r)+ (...

Aim of this paper is to study the parabolic Volterra equation u(t) + (b ∗Au)(t) = (QB)(t), t ≥ 0, on a separable Hilbert space. Throughout this work the operator −A is assumed to be a differential operator like the Laplacian, the elasticity operator, or the Stokes operator. The random disturbance Q1/2BH is modeled to be a system independent vector valued fractional Brownian motion with Hurst pa...