Truncated correlation and convolution operators is a general operator-class containing popular operators such as Toeplitz (WienerHopf), Hankel and nite interval convolution operators as well as small and big Hankel operators in several variables. We completely characterize the symbols for which such operators have nite rank, and develop methods for determining the rank in concrete cases. Such r...

Abstract. We find the minimum scale factor, for which the nonnegative Böttcher-Wenzel biquadratic form becomes a sum of squares (sos). To this we give the primal and dual solutions for the underlying semidefinite program. Moreover, for special matrix classes (tridiagonal, backward tridiagonal and cyclic Hankel matrices) we show that the above form is sos. Finally, we conjecture sos representabi...

This paper provides a new proof of the index formula for block Toeplitz operators. The idea is to calculate a certain integral formula for the winding number using Fourier series, expressing this in terms of Hankel operators, and producing the expected index.

Classically, formal orthogonal polynomials are studied with respect to a linear functional, which gives rise to a moment matrix with a Hankel structure. Moreover, in most situations, the moment matrix is supposed to be strongly regular. This implies a number of algebraic properties which are well known, like for example the existence of a three-term recurrence relation (characterised by a tridi...

We study the boundedness properties of truncation operators acting on bounded Hankel (or Toeplitz) infinite matrices. A relation with the Lacey-Thiele theorem on the bilinear Hilbert transform is established. We also study the behaviour of the truncation operators when restricted to Hankel matrices in the Schatten classes. 1. Statement of results In this note we will be dealing with infinite ma...

In this paper we deal with the subnormality and the quasinormality of Toeplitz operators with matrix-valued rational symbols. In particular, in view of Halmos’s Problem 5, we focus on the question: Which subnormal Toeplitz operators are normal or analytic ? We first prove: Let Φ ∈ L∞Mn be a matrix-valued rational function having a “matrix pole,” i.e., there exists α ∈ D for which kerHΦ ⊆ (z−α)H...

This paper provides the Banach duality theory structure of the optimal two-block H∞ problem. Alignment conditions are obtained and show that the optimal solution is flat in general, and unique in the SISO case. It is also proved that under specific conditions a Hankel-Toepltiz operator achieves its norm on the discrete spectrum, therefore generalizing a similar result obtained formerly for fini...

In this note, we study the notion of structured pseudospectra. We prove that for Toeplitz, circulant and symmetric structures, the structured pseudospectrum equals the unstructured pseudospectrum. We show that this is false for Hermitian and skew-Hermitian structures. We generalize the result to pseudospectra of matrix polynomials. Indeed, we prove that the structured pseudospectrum equals the ...