We prove the existence of tight frames whose elements lie on an arbitrary ellipsoidal surface within a real or complex separable Hilbert space H , and we analyze the set of attainable frame bounds. In the case whereH is real and has finite dimension, we give an algorithmic proof. Our main tool in the infinite dimensional case is a result we have proven which concerns the decomposition of a posi...

This paper furnishes two classes of methods for calculating the best approximate solution of an operator equation in Banach spaces, where the operator is bounded, linear and has closed range. The best approximate solution can be calculated by an iterative method in Banach spaces stated in terms of an operator parameter. Specifying the parameter yields some new and some old iterative techniques....

Let X = {X(t), t ∈ R+} be an operator stable Lévy process in R with exponent B, where B is an invertible linear operator on R. We determine the Hausdorff dimension and the packing dimension of the range X([0, 1]) in terms of the real parts of the eigenvalues of B. Running Title Dimension of Operator Stable Lévy Processes

In this paper, we investigate a perturbation of the Drazin inverse AD of a closed linear operator A; the main tool for obtaining the estimates is the gap between subspaces and operators. By (X) we denote the set of all closed linear operators acting on a linear subspace of X to X , where X is a complex Banach space. We write (A), (A), (A), ρ(A), σ(A), and R(λ,A) for the domain, nullspace, range...

Necessary and sufficent conditions are obtained for ¿(/-factorization of operators on /,. In particular it is shown that uniform invertibility of the compressions of the operator is not sufficient to insure an LU-factorization of the operator, thus answering a question of de Boor, Jia, and Pinkus. The question of when a bounded linear operator on lp, 1 < p <, oo, has an Li/-factorization has be...

We show that there exists an invertible frequently hypercyclic operator on $\ell^1(\mathbb{N})$ whose inverse is not hypercyclic.

Reversibility is a concept widely studied in physics and computer science. Quantum systems evolution is described by the time evolution operator U , which is unitary and then invertible. Likewise, reversible computation is characterized by means of invertible properties. Reversible/invertible cellular automata (CA) are one of the most relevant reversible computational models. Here we introduce ...