Complex symmetry of Toeplitz operators on the weighted Bergman spaces

Xiao-He Hu

The search session has expired. Please query the service again.

Displaying similar documents to “Complex symmetry of Toeplitz operators on the weighted Bergman spaces”

Schatten class generalized Toeplitz operators on the Bergman space

Chunxu Xu, Tao Yu (2021)

Czechoslovak Mathematical Journal

Similarity:

Let $μ$ be a finite positive measure on the unit disk and let $j \geq 1$ be an integer. D. Suárez (2015) gave some conditions for a generalized Toeplitz operator $T_{μ}^{(j)}$ to be bounded or compact. We first give a necessary and sufficient condition for $T_{μ}^{(j)}$ to be in the Schatten $p$ -class for $1 \leq p < \infty$ on the Bergman space $A^{2}$ , and then give a sufficient condition for $T_{μ}^{(j)}$ to be in the Schatten $p$ -class $(0 < p < 1)$ on $A^{2}$ . We also discuss the generalized Toeplitz operators with general bounded symbols. If $ϕ \in L^{\infty} (D, d A)$ and $1 < p < \infty$ , we define the generalized...

Area differences under analytic maps and operators

Mehmet Çelik, Luke Duane-Tessier, Ashley Marcial Rodriguez, Daniel Rodriguez, Aden Shaw (2024)

Czechoslovak Mathematical Journal

Similarity:

Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping $h$ and that of $z h$ , we study various $L^{2}$ norms for $T_{ϕ} (h)$ , where $T_{ϕ}$ is the Toeplitz operator with symbol $ϕ$ . In Theorem , given polynomials $p$ and $q$ we find a symbol $ϕ$ such that $T_{ϕ} (p) = q$ . We extend some of our results to the polydisc.

The generalized Toeplitz operators on the Fock space $F_{α}^{2}$

Chunxu Xu, Tao Yu (2024)

Czechoslovak Mathematical Journal

Similarity:

Let $μ$ be a positive Borel measure on the complex plane $ℂ^{n}$ and let $j = (j_{1}, \dots, j_{n})$ with $j_{i} \in ℕ$ . We study the generalized Toeplitz operators $T_{μ}^{(j)}$ on the Fock space $F_{α}^{2}$ . We prove that $T_{μ}^{(j)}$ is bounded (or compact) on $F_{α}^{2}$ if and only if $μ$ is a Fock-Carleson measure (or vanishing Fock-Carleson measure). Furthermore, we give a necessary and sufficient condition for $T_{μ}^{(j)}$ to be in the Schatten $p$ -class for $1 \leq p < \infty$ .

The relationship between $K_{u}^{2} \cap v H^{2}$ and inner functions

Xiaoyuan Yang (2024)

Czechoslovak Mathematical Journal

Similarity:

Let $u$ be an inner function and $K_{u}^{2}$ be the corresponding model space. For an inner function $v$ , the subspace $v H^{2}$ is an invariant subspace of the unilateral shift operator on $H^{2}$ . In this article, using the structure of a Toeplitz kernel $\ker T_{\bar{u} v}$ , we study the intersection $K_{u}^{2} \cap v H^{2}$ by properties of inner functions $u$ and $v$ $(v \neq u)$ . If $K_{u}^{2} \cap v H^{2} \neq {0}$ , then there exists a triple $(B, b, g)$ such that $\bar{u} v = \frac{λ b \bar{B O_{g}}}{g},$ where the triple $(B, b, g)$ means that $B$ and $b$ are Blaschke products, $g$ is an invertible function in $H^{\infty}$ , $O_{g}$ denotes the outer factor...

New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces

Xin-Cui Guo, Ze-Hua Zhou (2015)

Czechoslovak Mathematical Journal

Similarity:

Let $u$ be a holomorphic function and $ϕ$ a holomorphic self-map of the open unit disk $𝔻$ in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators $u C_{ϕ}$ from Zygmund type spaces to Bloch type spaces in $𝔻$ in terms of $u$ , $ϕ$ , their derivatives, and $ϕ^{n}$ , the $n$ -th power of $ϕ$ . Moreover, we obtain some similar estimates for the essential norms of the operators $u C_{ϕ}$ , from which sufficient and necessary conditions of compactness of $u C_{ϕ}$ follows immediately. ...

The boundedness of two classes of integral operators

Xin Wang, Ming-Sheng Liu (2021)

Czechoslovak Mathematical Journal

Similarity:

The aim of this paper is to characterize the $L^{p} - L^{q}$ boundedness of two classes of integral operators from $L^{p} (𝒰, d V_{α})$ to $L^{q} (𝒰, d V_{β})$ in terms of the parameters $a$ , $b$ , $c$ , $p$ , $q$ and $α$ , $β$ , where $𝒰$ is the Siegel upper half-space. The results in the presented paper generalize a corresponding result given in C. Liu, Y. Liu, P. Hu, L. Zhou (2019).

Linear maps preserving $A$ -unitary operators

Abdellatif Chahbi, Samir Kabbaj, Ahmed Charifi (2016)

Mathematica Bohemica

Similarity:

Let $ℋ$ be a complex Hilbert space, $A$ a positive operator with closed range in $ℬ (ℋ)$ and $ℬ_{A} (ℋ)$ the sub-algebra of $ℬ (ℋ)$ of all $A$ -self-adjoint operators. Assume $φ : ℬ_{A} (ℋ)$ onto itself is a linear continuous map. This paper shows that if $φ$ preserves $A$ -unitary operators such that $φ (I) = P$ then $ψ$ defined by $ψ (T) = P φ (P T)$ is a homomorphism or an anti-homomorphism and $ψ (T^{♯}) = ψ {(T)}^{♯}$ for all $T \in ℬ_{A} (ℋ)$ , where $P = A^{+} A$ and $A^{+}$ is the Moore-Penrose inverse of $A$ . A similar result is also true if $φ$ preserves $A$ -quasi-unitary operators in both directions such that there...

Controlling products of currents by higher powers of plurisubharmonic functions

Ahmad K. Al Abdulaali, Hassine El Mir (2020)

Czechoslovak Mathematical Journal

Similarity:

We discuss the existence of the current $g^{k} T$ , $k \in ℕ$ for positive and closed currents $T$ and unbounded plurisubharmonic functions $g$ . Furthermore, a new type of weighted Lelong number is introduced under the name of weight $k$ Lelong number.

Distance matrices perturbed by Laplacians

Balaji Ramamurthy, Ravindra Bhalchandra Bapat, Shivani Goel (2020)

Applications of Mathematics

Similarity:

Let $T$ be a tree with $n$ vertices. To each edge of $T$ we assign a weight which is a positive definite matrix of some fixed order, say, $s$ . Let $D_{i j}$ denote the sum of all the weights lying in the path connecting the vertices $i$ and $j$ of $T$ . We now say that $D_{i j}$ is the distance between $i$ and $j$ . Define $D : = [D_{i j}]$ , where $D_{i i}$ is the $s \times s$ null matrix and for $i \neq j$ , $D_{i j}$ is the distance between $i$ and $j$ . Let $G$ be an arbitrary connected weighted graph with $n$ vertices, where each weight is a positive definite matrix of order...