相关论文: The zero-product problem for Toeplitz operators wi…

Asymmetric truncated Toeplitz operators are compressions of multiplication operators acting between two model spaces. These operators are natural generalizations of truncated Toeplitz operators. In this paper we describe symbols of…

We study the weighted compactness and boundedness properties of Toeplitz operators on the Bergman space with respect to B\'ekoll\`e-Bonami type weights. Let $T_u$ denote the Toeplitz operator on the (unweighted) Bergman space of the unit…

This paper concerns the analysis of an unbounded Toeplitz-like operator generated by a rational matrix function having poles on the unit circle T. It extends the analysis of such operators generated by scalar rational functions with poles…

Let $p\in(0, 1]$. In this paper, the authors prove that a sublinear operator $T$ (which is originally defined on smooth functions with compact support) can be extended as a bounded sublinear operator from product Hardy spaces $H^p({{\mathbb…

We study polynomials with no zeros on the unit ball in complex Euclidean space with a view toward characterizing when a rational function is bounded on the ball. We give a complete local description of such polynomials in two variables near…

In this paper we characterize when the semi-commutator $T_fT_g-T_{fg}$ of two Toeplitz operators $T_f$ and $T_g$ on the Hardy space of the bidisc is zero. We also show that there is no nonzero finite rank semi-commutator on the bidisc.…

The geometric descriptions of the (essential) spectra of Toeplitz operators with piecewise continuous symbols are among the most beautiful results about Toeplitz operators on Hardy spaces $H^p$ with $1<p<\infty$. In the Hardy space $H^1$,…

In this paper we introduce and study the class of weighted multi-Toeplitz operators associated with noncommutative polydomains ${\bf D_f^m}$, ${\bf m}:=(m_1,\ldots, m_k)\in {\bf N}^k$, generated by $k$-tuples ${\bf f}:=(f_1,\ldots, f_k)$ of…

In this paper, we mainly study the necessary and sufficient conditions for the boundedness and compactness of Toeplitz operators on weighted Bergman spaces over a tubular domains by using the Carlson measures on tubular domains. We also…

This note is a follow-up to a recent paper by the author. Most of that theory is now realized in a new setting where the vector space of symbols is not necessarily an algebra nor is it equipped with an inner product, although it does have a…

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 study the spectrum of the product of two Toeplitz operators. Assume that the symbols of these operators are continuous and real-valued and that one of them is non-negative. We prove that the spectrum of the product of finite section…

Some new characterizations on Carleson measures for weighted Bergman spaces on the unit ball involving product of functions are obtained. For these we characterize bounded and compact Toeplitz operators between weighted Bergman spaces. The…

We discuss Toeplitz operators on the Segal-Bargmann space as functional realizations of anti-Wick operators on the Fock space. In the special case of radial symbols we exploit the isometric mapping between the Segal-Bargmann space and $l^2$…

Let L^k be a high power of a hermitian holomorphic line bundle over a complex manifold X. Given a differential form f on X, we define a super Toeplitz operator T(f) acting on the space of harmonic (0,q)-forms with values in L^k, with symbol…

Let $H$ be a Hilbert space of entire functions. Let $H'$ be the space of the functions $f(z)/\prod_i(z-z_i)$ where $f$ belongs to $H$ and vanishes at $n$ given complex points $z_i$. We compute a suitable $E$ function for $H'$ when one is…

In this note known formulas for the product of Toeplitz operators are revisited in the context of their applications to the study of Fredholmness, boundedness of Toeplitz products, and the Berezin-Toeplitz quantization. A few open problems…

For a given entire function $f(z)=\sum_{j=0}^{\infty}a_{j}z^{j}$, we study the zero distribution of $f_{r}(z)=\sum_{j\equiv r\pmod m}a_{j}z^{j}$ where $m\in\mathbb{N}$ and $0\le r<m$. We find conditions under which the zeros of $f_{r}(z)$…

A function is boundedly finite-to-one if there is a natural number $k$ such that each point has at most $k$ inverse images. In this paper, we prove in $\mathsf{ZF}$ (i.e., the Zermelo--Fraenkel set theory without the axiom of choice)…

We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding…