相关论文: The operator system of Toeplitz matrices
Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computation. The four classes have distinct features, but in 1990 we showed that Vandermonde and Hankel multipliers transform all these…
Truncated Toeplitz operators are compressions of Toeplitz operators on model spaces; they have received much attention in the last years. This survey article presents several recent results, which relate boundedness, compactness, and…
We study mapping properties of Toeplitz operators $T_\mu$ associated to nonnegative Borel measure $\mu$ on the complex space $\mathbb{C}^n$. We, in particular, describe the bounded and compact operators $T_\mu$ acting between Fock spaces in…
We find necessary and sufficient conditions for the product of two truncated Toeplitz operators on a model space to itself be a truncated Toeplitz operator, and as a result find a characterization for the maximal algebras of bounded…
We study the spectral norm of large rectangular random Toeplitz and circulant matrices with independent entries. For Toeplitz matrices, we show that the scaled norm converges to the norm of a bilinear operator defined via the pointwise…
Matrix valued truncated Toeplitz operators act on vector-valued model spaces. They represent a generalization of block Toeplitz matrices. A characterization of these operators analogue to the scalar case is obtained, as well as the…
Let $\mu_\alpha$ be the Lebesgue plane measure on the unit disk with the radial weight $\frac{\alpha+1}{\pi}(1-|z|^2)^\alpha$. Denote by $\mathcal{A}^{2}_{n}$ the space of the $n$-analytic functions on the unit disk, square-integrable with…
In this paper, we study matrix representations of truncated Toeplitz operators with respect to orthonormal bases which are invariant under a canonical conjugation map. In particular, we determine necessary and sufficient conditions for when…
This paper has aim to characterize Fredholmness and Weylness of upper triangular operator matrices having arbitrary dimension n. We present various characterization results in the setting of infinite dimensional Hilbert spaces, thus…
Chien, Liu, Nakazato, and Tam proved that all n by n classical Toeplitz matrices (one-level Toeplitz matrices) are unitarily similar to complex symmetric matrices via two types of unitary matrices and the type of the unitary matrices only…
We characterize the state space of a Toeplitz-Cuntz algebra TO_n in terms of positive operator matrices $\Omega$ on Fock space which satisfy sl(\Omega) \le \Omega, where sl(\Omega) is the operator matrix obtained from \Omega by taking the…
In this note, we study the fast solution of Toeplitz linear systems with coefficient matrix $T_n(f)$, where the generating function $f$ is nonnegative and has a unique zero at zero of any real positive order $\theta$. As preconditioner we…
We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for these operators to be Fredholm. We further construct a Fredholm concave corner Toeplitz…
We present two novel results about Hilbert space operators which are nilpotent of order two. First, we prove that such operators are indestructible complex symmetric operators, in the sense that tensoring them with any operator yields a…
By establishing some reproducing kernel estimates, we characterize the bounded, compact and Schatten $p$-class Toeplitz operators with positive measure symbols on the weighted Fock space $F^2_{\alpha,w}$ for $p\geq1$, where $w$ is a weight…
New algorithms are presented for computing annihilating polynomials of Toeplitz, Hankel, and more generally Toeplitz+ Hankel-like matrices over a field. Our approach follows works on Coppersmith's block Wiedemann method with structured…
This paper is devoted to semi-classical aspects of symplectic reduction. Consider a compact prequantizable Kahler manifold M with a Hamiltonian torus action. Guillemin and Sternberg introduced an isomorphism between the invariant part of…
For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a power (possibly fractional) of a defining function, and, more generally, of the…
Conditions are established under which Fredholmness, Coburn's property and one- or two-sided invertibility are shared by a Toeplitz operator with matrix symbol $G$ and the Toeplitz operator with scalar symbol $\det G$. These results are…
Truncated Toeplitz operators are C--symmetric with respect to the canonical conjugation given on an appropriate model space. However, by considering only one conjugation one cannot characterize truncated Toeplitz operators. It will be…