调和Dirichlet空间上小Hankel算子的乘积(英文)

研究了调和Dirichlet空间上调和符号的小Hankel算子的乘积,给出了此类小Hankel算子交换性和乘积为零的完全刻画.     

调和Dirichlet空间上的Toeplitz算子

刻画了调和Dirichlet空间上Toeplitz算子的有界性、紧性,讨论了Toeplitz算子的代数性质,得到了Toeplitz代数与Hankel代数的短正合列.还计算了Toeplitz代数与Hankel代数中Fredholm算子的Fredholm指标,得到了Toeplitz代数与Hankel代数的K_0与K_1群.     

Dirichlet空间上Toeplitz算子的交换性(Ⅱ)

首先讨论了Ω符号的Toeplitz算子在Dirichlet空间D2上的交换性,推广了有界调和符号情形,也给出了不同于经典Hardy空间或Bergman空间上交换性的新情形;其次给山了L∞θ.1符号Toeplitz算于与径向或拟齐次符号的Toeplitz算于可交换的充要条件.所得结果与Hardy空间,Bergman空间以及Dirichlet空间D均有不同.     

多重调和Bergman空间上的Toeplitz算子和Hankel算子

完全刻画多重调和Bergman空间上Toeplitz算子和Hankel算子的紧性.运用紧Toeplitz算子这个结果,建立了Toeplitz代数和小Hankel代数的短正合列,推广了单位圆盘上相应的结果.     

Dirichlet空间上Toeplitz算子与Berezin型变换相关的一些性质

本文研究了单位圆盘D 的Dirichlet 空间上Toeplitz 算子和小Hankel 算子. 利用Berezin 型变换讨论了Toeplitz 算子的不变子空间问题, 具有Berezin 型符号的Toeplitz 算子的渐进可乘性以及Toeplitz 算子的Riccati 方程的可解性. 应用Berezin 变换得到了Toeplitz 算子和小Hankel 算子可逆的充分条件. 此外, 还利用Hankel 算子和Berezin 变换刻画了算子2T_uv-T_uT_v-T_vT_u 的紧性, 其中函数u,v ∈ L^2,1.     

Bergman空间上可交换的Hankel算子和Toeplitz算子

证明了Bergman空间上的两个小Hankel算子如果是可交换的且其中一个是拟齐次的小Hankel算子,则另一个也是拟齐次的.还研究了Toeplitz算子和小Hankel算子的交换性.     

单位球Dirichlet空间上的交换对偶Toeplitz算子

研究对偶Toeplitz算子（半）交换时其符号的关系.通过对其符号的分解,借助多复变函数的有关理论,得到了单位球Dirichlet空间上以多重调和函数为符号的对偶Toeplitz算子Sψ与Sψ（半）交换的充要条件.     

调和Dirichlet空间D_h~1上有界、紧与Fredholm的Toeplitz算子

该文讨论了调和Dirichlet空间D_h~1上Toeplitz与Hankel算子的有界性、紧性与Fredholm性质,计算了Toeplitz算子的Fredholm指标.     

带有调和符号的交换Toeplitz算子

我们研究作用于调和Bergman空间b²(D{0})上的带有调和符号的Toeplitz算子,其中D是复平面上的单位圆盘.首先,研究b^p(Ω)的结构并且获得b^p(Ω)中的每个元在调和Bergman投影之下的像.其次,证明特殊的Toeplitz算子T_log|w|:b²(D{0})→b²(D/{0})是有界线性算子并获得带有调和或全纯符号的Toeplitz算子与T_log|w|可交换的充分必要条件.第三,我们获得两个带有全纯符号的Toeplitz算子可交换的充分必要条件.第四,给出带有全纯符号的正规Toeplitz算子的一个特征.最后,得到带有调和符号的Toeplitz算子彼此之间可交换的一个必要条件.     

Dirichlet型空间上Hankel算子和乘法算子

本文讨论了Dirichlet型空间上的再生核,并对Dirichlet型空间上乘法算了,Hankel算子和小Hankel算子的基本性质进行了研究,同时也给出了这些算子的有界性,紧性和Schatten理想的初步刻画.     

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.     

Operators on the orthogonal complement of the Dirichlet space

In this paper we prove that a dual Hankel operator is zero if and only if its symbol is orthogonal to the Dirichlet space in the Sobolev space, and characterize the symbols for (semi-)commuting dual Toeplitz operators on the orthogonal complement of the Dirichlet space in Sobolev space.     

Dirichlet空间上的Bergman型Toeplitz算子

本文给出了Dirichlet空间上以有界调和函数为符号的Bergman型Toeplitz算子是紧算子的充要条件.同时刻画了此类Bergman型Toeplitz算子在Dirichlet空间上的交换性.     

Dirichlet空间上Bergman型Toeplitz算子的代数性质

本文讨论了Dirichlet空间上由调和函数诱导的Bergman型Toeplitz算子的基本性质和代数性质,包括此类算子的自伴性、乘积性质、交换性及可逆性,并计算了算子的谱.     

Commuting Toeplitz operators on the Dirichlet space

In this paper, we study the commutativity of Toeplitz operators with continuous symbols on the Dirichlet space. First, under a mild condition concerning absolute continuity we characterize (semi-)commuting Toeplitz operators. This is a generalization of the case of harmonic symbols. Also, if one of the symbol is radial or analytic, we get another characterization, which is different from the case on the Bergman space.     

Product of Toeplitz operators on the harmonic Dirichlet space

In this paper, we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product of two Toeplitz operators is another Toeplitz operator only if one factor is constant.     

Toeplitz算子在Dirichlet空间上的亚正规性

In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,respectively.We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant.     

Commutativity of Toeplitz operators on the harmonic Dirichlet space

In this paper, we completely characterize (semi-)commutativity of Toeplitz operators with harmonic symbols on harmonic Dirichlet space.     

Algebraic properties of Toeplitz operators on the Dirichlet space

We study some algebraic properties of Toeplitz operators on the Dirichlet space. We first characterize (semi-)commuting Toeplitz operators with harmonic symbols. Next we study the product problem of when product of two Toeplitz operators is another Toeplitz operator. As an application, we show that the zero product of two Toeplitz operators with harmonic symbol has only a trivial solution. Also, the corresponding compact product problem is studied.