In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define a new notion of diagonalization for these operators, which we call s-diagonalization. We ...

Given a bounded positive linear operator A on a Hilbert space H we consider the semi-Hilbertian space (H, <,>_A), where <ℇ, n >_A =< Aℇ,n>. On the other hand, we consider the operator range R(A^1/2) with its canonical ...

In the present paper we study different conditions regarding the sum of operator ranges. In particular, we find conditions on operators A, B which imply that R(A+B)=R(A)+R(B) and derive some results concerning projections.

Let CR be the set of all bounded linear operators between Hilbert spaces H, K with closed range. This paper is devoted to the study of the topological properties of CR if certain natural metrics are considered on it. We ...

In this note, we solve the dynamical sampling problem for a class of shift-preserving operators L:V→V acting on a finitely generated shift-invariant space V. We find conditions on L and a finite set of functions of V so ...

A problem that humans must face very often is that of having to add, melt or synthesize information, that is, combine together a series of data from various sources to reach a certain conclusion or make a certain decision. ...