Hyponormal Toeplitz Operators Research Articles

Remarks on hyponormal Toeplitz operators with nonharmonic symbols

Abstract In this article, we present some necessary or sufficient conditions for the hyponormality of Toeplitz operator T φ {T}_{\varphi } on the Bergman space A 2 ( D ) {A}^{2}\left({\mathbb{D}}) . In particular, we consider the Toeplitz operator T φ {T}_{\varphi } with nonharmonic symbols φ \varphi under certain assumptions.

Hyponormal Toeplitz operators with non-harmonic symbols on the weighted Bergman spaces

In this paper, we consider the hyponormality of Toeplitz operators acting on the weighted Bergman space A_{alpha }^2({mathbb{D}}). We establish necessary or sufficient conditions for the hyponormality of Toeplitz operators with non-harmonic symbols varphi (z) that are bivariate polynomials in z and {overline{z}} (i.e., varphi (z)=az^m{overline{z}}^n+bz^s{overline{z}}^t). In particular, we present some characteristics according to the coefficients and degree of varphi (z).

Hyponormal Toeplitz Operators with Non-harmonic Symbols on the Generalized Derivative Hardy Space

Hyponormal Toeplitz Operators with Non-harmonic Symbols on the Generalized Derivative Hardy Space

Remarks on Hyponormal Toeplitz Operators on the Weighted Bergman Spaces

In this paper, we study the hyponormal Toeplitz operators $$T_{\varphi }$$ , where $$\varphi $$ is a trigonometric polynomial symbol with finite degree. We present necessary and sufficient conditions for the hyponormality of $$T_{\varphi }$$ under some assumptions about the coefficients of $$\varphi $$ . Next, we find the necessary condition for hyponormality of $$T_{\varphi }$$ .

Hyponormal Toeplitz operators with non-harmonic algebraic symbol

Given a bounded function $$\varphi $$ on the unit disk in the complex plane, we consider the operator $$T_{\varphi }$$, defined on the Bergman space of the disk and given by $$T_{\varphi }(f)=P(\varphi f)$$, where P denotes the orthogonal projection to the Bergman space in $$L^2({\mathbb {D}},dA)$$. For algebraic symbols $$\varphi $$, we provide new necessary conditions on $$\varphi $$ for $$T_{\varphi }$$ to be hyponormal, extending recent results of Fleeman and Liaw. Our approach is perturbative and aims to understand how small changes to a symbol preserve or destroy hyponormality of the corresponding operator. We consider both additive and multiplicative perturbations of a variety of algebraic symbols. One of our main results provides a necessary condition on the complex constant C for the operator $$T_{z^n+C|z|^s}$$ to be hyponormal. This condition is also sufficient if $$s\ge 2n$$.

Hyponormal Toeplitz operators with non-harmonic Symbol acting on the Bergman space

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 the study of hyponormal Toeplitz operators acting on $A^{2}(\mathbb{D})$, as well as give results for when $\varphi$ is a non-harmonic polynomial. We include a first investigation of Putnam's inequality for hyponormal operators with non-analytic symbols. Particular attention is given to unusual hyponormality behavior that arises due to the extension of the class of allowed symbols.

Self-commutator norm of hyponormal Toeplitz operators

Self-commutator norm of hyponormal Toeplitz operators

Hyponormality of Toeplitz operators in several variables by the weighted shifts approach

ABSTRACT In this paper, we characterize hyponormality of a class of operators related to a tuple of weighted shifts. As applications we construct examples of hyponormal Toeplitz operators on Hilbert spaces of holomorphic functions on the polydisk or the unit ball which include the Bergman space of the polydisk, the Hardy space of the unit ball and the Drury-Arveson space.

A note on the spectral area of Toeplitz operators

In this note, we show that for hyponormal Toeplitz operators, there exists a lower bound for the area of the spectrum. This extends the known estimate for the spectral area of Toeplitz operators with an analytic symbol.

Hyponormal Toeplitz operators with polynomial symbols on weighted Bergman spaces

Abstract In this note we consider the hyponormality of Toeplitz operators T φ on weighted Bergman space A α 2 ( D ) with symbol in the class of functions f + g ¯ with polynomials f and g. MSC:47B20, 47B35.

Hyponormal trigonometric Toeplitz operators

We investigate hyponormal Toeplitz operators Tφ with trigonometric polynomial symbols φ via the Caratheodory-Schur Interpolation Problem. We present several formulae for computing the rank of the selfcommutator [T ∗ φ ,Tφ ] in the cases where Tφ is a hyponormal operator. In addition we consider the hyponormal extension problem of Toeplitz operators. Mathematics subject classification (2010): Primary 47B20, 47B35, 47A20.

Hyponormal Toeplitz operators and zeros of polynomials

The problem of hyponormality for Toeplitz operators with (trigonometric) polynomial symbols is studied. We give a necessary and sufficient condition using the zeros of the analytic polynomial induced by the Fourier coefficients of the symbol.

On a class of jointly hyponormal Toeplitz operators

We characterize when a pair of Toeplitz operators T = (T Φ , T ψ ) is jointly hyponormal under various assumptions--for example, Φ is analytic or Φ is a trigonometric polynomial or Φ - ψ is analytic. A typical characterization states that T = (T Φ , T ψ ) is jointly hyponormal if and only if an algebraic relation of Φ and ψ holds and the single Toeplitz operator T ω is hyponormal, where ω is a combination of Φ and ψ. More general results for an n-tuple of Toeplitz operators are also obtained.

On hyponormal toeplitz operators with polynomial and symmetric-type symbols

This paper treats the hyponormality of Toeplitz operators that have polynomial symbols with symmetric-type sets of coefficients.

On hyponormal Toeplitz operators with polynomial and circulant-type symbols

This paper characterises those hyponormal Toeplitz operators on the Hardy space of the unit circle among all Toeplitz operators that have polynomial symbols with circulant-type sets of coefficients.

Hyponormality and spectra of Toeplitz operators

This paper concerns algebraic and spectral properties of Toeplitz operators T φ T_{\varphi } , on the Hardy space H 2 ( T ) H^{2}({\mathbb {T}}) , under certain assumptions concerning the symbols φ ∈ L ∞ ( T ) \varphi \in L^{\infty }({\mathbb {T}}) . Among our algebraic results is a characterisation of normal Toeplitz opertors with polynomial symbols, and a characterisation of hyponormal Toeplitz operators with polynomial symbols of a prescribed form. The results on the spectrum are as follows. It is shown that by restricting the spectrum, a set-valued function, to the set of all Toeplitz operators, the spectrum is continuous at T φ T_{\varphi } , for each quasicontinuous φ \varphi . Secondly, we examine under what conditions a classic theorem of H. Weyl, which has extensions to hyponormal and Toeplitz operators, holds for all analytic functions of a single Toeplitz operator with continuous symbol.

Hyponormal Toeplitz operators with polynomial symbols

Hyponormal Toeplitz operators with polynomial symbols

A Generalization of Cowen′s Characterization of Hyponormal Toeplitz Operators

In this paper we extend an elegant result of C. C. Cowen [ Proc. Amer. Math. Soc. 103 (1988), 809-812] on the hyponormality of Toeplitz operators to a class of (generalized) Toeplitz operators. In order to do this by a commutant lifting approach we study the operator equation H A = H BT C , where H A , H B are (generalized) Hankel operators and T C is an analytic Toeplitz operator. Related results about the range inclusion of Hankel and Toeplitz operators are also obtained.

Hyponormal Toeplitz Operators and Extremal Problems of Hardy Spaces

The symbols of hyponormal Toeplitz operators are completely described and those are also studied, being related with the extremal problems of Hardy spaces. Moreover, we discuss Halmos's question about a subnormal Toeplitz operator when the self-commutator is finite rank

Hyponormal Toeplitz operators and extremal problems of Hardy spaces

The symbols of hyponormal Toeplitz operators are completely described and those are also studied, being related with the extremal problems of Hardy spaces. Moreover, we discuss Halmos’s question about a subnormal Toeplitz operator when the self-commutator is finite rank.