Block dual Toeplitz Operators on the Orthogonal Complements of Fock Spaces

In this paper,we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces,and the compactness of the finite sum of two dual Toeplitz operators products.The commutator and semi-commutator induced by the block dual Toeplitz operators are considered.

Reducing Subspaces of Toeplitz Operators Induced by a Class of Non-analytic Monomials over the Unit Ball

In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each minimal reducing subspace M is finite dimensional,and if dim M≥3,then M is induced by a monomial.Furthermore,the structure of commutant algebra v(T_(w)N_(z)N):={M^(*)_(w)NM_(z)N,M^(*)_(z)NM_(w)N}′is determined by N and the two dimensional minimal reducing subspaces of(T_(w)N_(z)N.We also give some interesting examples.

Commuting Dual Toeplitz Operators on Weighted Bergman Spaces of the Unit Ball

In this paper, we study the commutativity of dual Toeplitz operators on weighted Bergman spaces of the unit ball. We obtain the necessary and sufficient conditions for the commutativity, essential commutativity and essential semi-commutativity of dual Toeplitz operator on the weighted Bergman spaces of the unit ball.

Toeplitz Operators on Dirichlet Spaces

In this paper we study Toeplitz operators on Dirichlet spaces and describe the boundedness and compactness of Toeplitz operators on Dirichlet spaces. Meanwhile, we give density theorems for Toeplitz operators on Dirichlet spaces

Compact Toeplitz Operators on the Weighted Dirichlet Space

In this paper, we completely characterize the compactness of Toeplitz operators with con- tinuous symbol on the weighted Dirichlet space.

Difference of Composition Operators on Some Analytic Function Spaces

For two analytic self-mapsφandψdefined on the unit disk D,we characterize completely the boundedness and compactness of the difference Cφ-Cψof the composition operators Cφand Cψfrom Bloch space B into Besov space Bν∞.Moreover,we also give a complete characterization of the compactness of the difference Cφ-Cψon BMOA space.

Algebraic Properties of Toeplitz and Small Hankel Operators on the Harmonic Bergman Space

In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.Meanwhile,we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.

Commuting Dual Toeplitz Operators on the Harmonic Dirichlet Space

In this paper, we characterize the symbols for （semi-）commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for φ ,ψ ∈ W1, ∞, SφSψ = SψSφ on （Dh）⊥ if and only if φ and ψ satisfy one of the following conditions： （1） Both φ and ψ are harmonic functions; （2） There exist complex constants α and β, not both O, such that φ = αφ＋β.

Toeplitz Operators with BMO Symbols on the Weighted Bergman Space of the Unit Ball

In this paper we prove that the boundedness and compactness of Toeplitz operator with a BMOα1 symbol on the weighted Bergman space Aα2（Bn） of the unit ball is completely determined by the behavior of its Berezin transform, where ≥ -1 and n 〉 1.

Super Weak Compactness and Uniform Eberlein Compacta

We prove that a topological space is uniform Eberlein compact iff it is homeomorphic to a super weakly compact subset C of a Banach space such that the closed convex hull coC of C is super weakly compact. We also show that a Banach space X is super weakly compactly generated iff the dual unit ball B;of X;in its weak star topology is affinely homeomorphic to a super weakly compactly convex subset of a Banach space.

Radial Operators on the Weighted Bergman Spaces over the Polydisk

In this paper, we study radial operators in Toeplitz algebra on the weighted Bergman spaces over the polydisk by the(m, λ)-Berezin transform and find that a radial operator can be approximated in norm by Toeplitz operators without any conditions. We prove that the compactness of a radial operator is equivalent to the property of vanishing of its(0, λ)-Berezin transform on the boundary. In addition, we show that an operator S is radial if and only if its(m, λ)-Berezin transform is a separately radial function.

Properties of Toeplitz Operators on the Dirichlet Space Over the Ball

On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero.

Hyponormal Toeplitz Operators on the Polydisk

By bounded vector-valued functions and block matrix representations of Hankel operators, we completely characterize the hyponormality of Toeplitz operators on the Hardy space of the polydisk.

Commuting Toeplitz Operators on the Hardy Space of the Polydisk

In this paper, we show that two Toeplitz operators Tf and Tg on the Hardy space of the polydisk can commute if and only if the Berezin transform of the commutator [Tf, Tg] is n-harmonic.

The Root Operator on Invariant Subspaces of the Weighted Bergman Space

In this paper, for an invariant subspace I of the weighted Bergman space, the weighted root operator is defined. We study the weighted root operator and obtain its fundamental properties when the invariant subspace I has finite index. Furthermore, we give some examples of the root operator and estimate ranks of the operators.