相关论文: Otto Toeplitz: Algebraiker der unendlichen Matrize…
This work was originally published by the author in 1999 in a book [1] and later became part of the author's doctoral thesis in 1999 [2]. Since the original language of these works is not English, the author provides a translation of the…
We consider commutative C* -algebras of Toeplitz operators in the weighted Bergman space on the unit ball in $\mathbb{C}^{\mathbf{n}}$. For the algebras of elliptic type we find a new representation, namely as the algebra of operators which…
We study for the first time the action of the Hilbert matrix $$\mathcal H=(c_{n,k})_{n,k\geq 0}, \quad c_{n,k}=\frac{1}{n+k+1}$$ on the analytic tent spaces $AT^q_p, 1<p,q <\infty,$ of the unit disc $\mathbb D$ of the complex plane. They…
multiplication operator on a Hilbert space may be approximated with finite sections by choosing an orthonormal basis of the Hilbert space. Nonzero multiplication operators on $L^2$ spaces of functions are never compact and then such…
Unbounded (and bounded) Toeplitz operators (TO) with rational symbols are analysed in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains,…
We study invertibility and compactness of positive Toeplitz operators associated to a continuous Parseval frame on a Hilbert space. As applications, we characterize compactness of affine and Weyl-Heisenberg localization operators as well as…
We determine the ideal structure of the Toeplitz C*-algebra on the bidisk.
We study positive Toeplitz operators on the Bergman spaces having the fast decreasing weight functions in a certain class. We give the characterizations for the boundedness and compactness of Toeplitz operators in terms of their Berezin…
Given an infinite, compact, monothetic group $G$ we study decompositions and structure of unbounded derivations in a crossed product C$^*$-algebra $C(G)\rtimes\Z$ obtained from a translation on $G$ by a generator of a dense cyclic subgroup.…
We consider symmetric separately radial (with corresponding group $S_n\rtimes \mathbb{T}^n$) and alternating separately radial (with corresponding group $A_n\rtimes \mathbb{T}^n$) symbols, as well as the associated Toeplitz operators on the…
Let $(X, T^{1,0}X)$ be a connected orientable compact CR manifold of dimension $2n+1$, $n \geq 1$ with non-degenerate Levi curvature. In this paper, we study the algebra of Toeplitz operators on $X$ and we establish star product for some…
Hilbert's Nullstellensatz is one of the most fundamental correspondences between algebra and geometry, and has inspired a plethora of noncommutative analogs. In last two decades, there has been an increased interest in understanding…
We define a determinant on the Toeplitz algebra associated to a minimal flow, give a formula for this determinant in terms of symbols, and show that this determinant can be used to give information about the algebraic $K$-theory of…
The set of infinite upper-triangular totally positive Toeplitz matrices has a classical parametrisation proved by Edrei et al and originally conjectured by Schoenberg, that involves pairs of sequences of positive real parameters. These…
Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…
We study the Fourier--Stieltjes algebra of Roelcke precompact, non-archimedean, Polish groups and give a model-theoretic description of the Hilbert compactification of these groups. We characterize the family of such groups whose…
This is a first paper by the authors dedicated to the distribution of eigenvalues for random perturbations of large bidiagonal Toeplitz matrices.
We find a relation guaranteeing that Hankel operators realized in the space of sequences $\ell^2 ({\Bbb Z}_{+}) $ and in the space of functions $L^2 ({\Bbb R}_{+}) $ are unitarily equivalent. This allows us to obtain exhaustive spectral…
We investigate the joint convergence of independent random Toeplitz matrices with complex input entries that have a pair-correlation structure, along with deterministic Toeplitz matrices and the backward identity permutation matrix.…
We review the theory of Toeplitz extensions and their role in operator K-theory, including Kasparov's bivariant K-theory. We then discuss the recent applications of Toeplitz algebras in the study of solid state systems, focusing in…