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### A Berezin-type map and a class of weighted composition operators

Concrete Operators

In this paper we consider the map L defined on the Bergman space [...] of the right half plane [...] .

### A class of integral operators on mixed norm spaces in the unit ball

Czechoslovak Mathematical Journal

This article provided some sufficient or necessary conditions for a class of integral operators to be bounded on mixed norm spaces in the unit ball.

### A Hankel matrix acting on Hardy and Bergman spaces

Studia Mathematica

Let μ be a finite positive Borel measure on [0,1). Let ${ℋ}_{\mu }={\left({\mu }_{n,k}\right)}_{n,k\ge 0}$ be the Hankel matrix with entries ${\mu }_{n,k}={\int }_{\left[0,1\right)}{t}^{n+k}d\mu \left(t\right)$. The matrix ${}_{\mu }$ induces formally an operator on the space of all analytic functions in the unit disc by the fomula ${ℋ}_{\mu }\left(f\right)\left(z\right)={\sum }_{n=0}^{\infty }i\left({\sum }_{k=0}^{\infty }{\mu }_{n,k}{a}_{k}\right)zⁿ$, z ∈ , where $f\left(z\right)={\sum }_{n=0}^{\infty }aₙzⁿ$ is an analytic function in . We characterize those positive Borel measures on [0,1) such that ${ℋ}_{\mu }\left(f\right)\left(z\right)={\int }_{\left[0,1\right)}f\left(t\right)/\left(1-tz\right)d\mu \left(t\right)$ for all f in the Hardy space H¹, and among them we describe those for which ${ℋ}_{\mu }$ is bounded and compact on H¹. We also study the analogous problem for the Bergman space A².

### A K-theoretic relative index theorem and Callias-type Dirac operators.

Mathematische Annalen

### A maximum problem for operators

Časopis pro pěstování matematiky

### A model for some analytic Toeplitz operators

Studia Mathematica

We present a change of variable method and use it to prove the equivalence to bundle shifts for certain analytic Toeplitz operators on the Banach spaces ${H}^{p}\left(G\right)\left(1\le p<\infty \right)$. In Section 2 we see this approach applied in the analysis of essential spectra. Some partial results were obtained in  in the Hilbert space case.

### A model for Toepliz operators in the space of entire functions of exponential type

Bulletin de la Société Mathématique de France

### A new look on Hankel forms over Fock space

Studia Mathematica

### A note on Toeplitz operators on Bergman spaces

Commentationes Mathematicae Universitatis Carolinae

### A proof of Nehari's theorem through the coefficient of a matricial measure.

Divulgaciones Matemáticas

### A remark to a paper of Janas “Toeplitz operators related to certain domains in ${C}^{n}$”

Studia Mathematica

### A Reproducing Kernel and Toeplitz Operators in the Quantum Plane

Communications in Mathematics

We define and analyze Toeplitz operators whose symbols are the elements of the complex quantum plane, a non-commutative, infinite dimensional algebra. In particular, the symbols do not come from an algebra of functions. The process of forming operators from non-commuting symbols can be considered as a second quantization. To do this we construct a reproducing kernel associated with the quantum plane. We also discuss the commutation relations of creation and annihilation operators which are defined...

### A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

Concrete Operators

We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.

### A simple proof of the classification of normal Toeplitz matrices.

ELA. The Electronic Journal of Linear Algebra [electronic only]

### A theorem of Nehari type on weighted Bergman spaces of the unit ball.

Abstract and Applied Analysis

### About the generating function of a left bounded integer-valued random variable

Bulletin de la Société Mathématique de France

We give a relation between the sign of the mean of an integer-valued, left bounded, random variable $X$ and the number of zeros of $1-\Phi \left(z\right)$ inside the unit disk, where $\Phi$ is the generating function of $X$, under some mild conditions

### Algebraic properties of Toeplitz operators on weighted Bergman spaces

Czechoslovak Mathematical Journal

We study algebraic properties of two Toeplitz operators on the weighted Bergman space on the unit disk with harmonic symbols. In particular the product property and commutative property are discussed. Further we apply our results to solve a compactness problem of the product of two Hankel operators on the weighted Bergman space on the unit bidisk.

### Algebras of singular integral operators on rearrangement-invariant spaces and Nikolski ideals.

The New York Journal of Mathematics [electronic only]

### Algebras of Toeplitz operators with oscillating symbols.

Revista Matemática Iberoamericana

This paper is devoted to Banach algebras generated by Toeplitz operators with strongly oscillating symbols, that is, with symbols of the form b[eia(x)] where b belongs to some algebra of functions on the unit circle and a is a fixed orientation-preserving homeomorphism of the real line onto itself. We prove the existence of certain interesting homomorphisms and establish conditions for the normal solvability, Fredholmness, and invertibility of operators in these algebras.

### An Application of the Theorem of Rudin to the Toeplitz Operators on Odd Spheres.

Mathematische Zeitschrift

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