Related papers: Finite Rank Perturbations of Toeplitz Products on …

We study the weighted compactness and boundedness of Toeplitz operators on the Fock spaces. Fix $\alpha>0$. Let $T_{\varphi}$ be the Toeplitz operator on the Fock space $F^2_{\alpha}$ over $\mathbb{C}^n$ with symbol $\varphi\in L^{\infty}$.…

Given $T\subset\mathbb{R}$ and a metric space $M$, we introduce a nondecreasing sequence of pseudometrics $\{\nu_n\}$ on $M^T$ (the set of all functions from $T$ into $M$), called the \emph{joint modulus of variation}. We prove that if two…

Let $\lambda$ be a complex number in the closed unit disc $\overline{\Bbb D}$, and $\cal H$ be a separable Hilbert space with the orthonormal basis, say, ${\cal E}=\{e_n:n=0,1,2,\cdots\}$. A bounded operator $T$ on $\cal H$ is called a {\em…

In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…

For any given bounded symmetric domain, we prove the existence of commutative $C^*$-algebras generated by Toeplitz operators acting on any weighted Bergman space. The symbols of the Toeplitz operators that generate such algebras are defined…

Consider the pairs $(f,G)$ with $f = f(x_1,\dots,x_N)$ being a polynomial defining a quasihomogeneous singularity and $G$ being a subgroup of ${\rm SL}(N,\mathbb{C})$, preserving $f$. In particular, $G$ is not necessary abelian. Assume…

We study means of geometric type of quasi-Toeplitz matrices, that are semi-infinite matrices $A=(a_{i,j})_{i,j=1,2,\ldots}$ of the form $A=T(a)+E$, where $E$ represents a compact operator, and $T(a)$ is a semi-infinite Toeplitz matrix…

In this paper we study some basic problems about Toeplitz subshifts of finite topological rank. We define the notion of a strong Toeplitz subshift of finite rank $K$ by combining the characterizations of Toeplitz-ness and of finite…

We consider the Jacobi operator (T,D(T)) associated with an indeterminate Hamburger moment problem, i.e., the operator in $\ell^2$ defined as the closure of the Jacobi matrix acting on the subspace of complex sequences with only finitely…

Prony's problem in several variables has attracted some attention recently and provides an interesting combination of polynomial ideal theory with analytic and numeric computations. This note points out further connections to Hankel…

We consider the Toeplitz operator with symbol z^n+C|z|^s acting on certain weighted Bergman spaces and determine for what values of the constant C this operator is hyponormal. The condition is presented in terms of the norm of an explicit…

This paper presents a comprehensive study of H-Toeplitz operators on the Fock space, a class of operators that synthesizes structural elements of both Toeplitz and Hankel operators. We derive explicit matrix representations for these…

The Toeplitz operator acting on the Bergman space $A^{2}(\mathbb{D})$, with symbol $\varphi$ is given by $T_{\varphi}f=P(\varphi f)$, where $P$ is the projection from $L^{2}(\mathbb{D})$ onto the Bergman space. We present some history on…

We prove that, given a constant $K> 2$ and a bounded linear operator $T$ from a JB$^*$-triple $E$ into a complex Hilbert space $H$, there exists a norm-one functional $\psi\in E^*$ satisfying $$\|T(x)\| \leq K \, \|T\| \, \|x\|_{\psi},$$…

In this paper we prove that if S equals a finite sum of finite products of Toeplitz operators on the Bergman space of the unit disk, then S is compact if and only if the Berezin transform of S equals 0 on the boundary of the disk. This…

In this paper, we consider weighted Bergman spaces $\mathcal{B}_{\alpha,p}$ of log-subharmonic functions on the unit sphere. Using the isoperimetric inequality for the spherical metric we prove certain monotonicity property for super-level…

We introduce a canonical operator-theoretic construction associated to a finite geometric lattice, in which a simple nonassociative ``diamond product'' on the lattice basis gives rise to a family of creation operators indexed by atoms and a…

One of the major goals in the theory of Toeplitz operators on the Bergman space over the unit disk $\mathbb{D}$ in the complex place $\mathbb{C}$ is to completely describe the commutant of a given Toeplitz operator, that is, the set of all…

Let $a(z)=\sum_{i\in\mathbb Z}a_iz^i$ be a complex valued function defined for $|z|=1$, such that $\sum_{i\in\mathbb Z}|ia_i|<\infty$, and let $E=(e_{i,j})_{i,j\in\mathbb {Z}^+}$ be such that $\sum_{i,j\in\mathbb{Z}^+}|e_{i,j}|<\infty$. A…

For self-adjoint Hankel operators of finite rank, we find an explicit formula for the total multiplicity of their negative and positive spectra. We also show that very strong perturbations, for example, a perturbation by the Carleman…