加权解析函数空间上Toeplitz算子  

Toeplitz Operators on Weighted Analytic Function Spaces

作　　者：巫舒敏 夏锦[1] WU Shumin;XIA Jin(School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学数学与信息科学学院,广州510006

出　　处：《四川轻化工大学学报（自然科学版）》2021年第4期90-100,共11页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金项目(11971125)。

摘　　要：文章由两部分构成。第一部分主要研究了复平面C上向量值DoublingFock空间F^(2)ϕ上以L(H)-值正算子值函数G(z)为符号的Teoplitz算子,其中ϕ为次调和函数,且dν=ΔϕdA为非零加倍测度,Δϕ≃1/ρ^(2),通过得到的满足Carleson条件以及消失Carleson条件的几个等价刻画,并且利用Carleson条件刻画了具有L(H)-值正算子值函数符号G(z)的Toeplitz算子的有界性与紧性的几个等价条件。第二部分研究了单位圆盘D上正规权Bergman空间A^(2)β上符号在L∞上的Toeplitz算子的本性范数,算子A的本性范数表示为||A||e=inf B∈K(D){||A-B||},其中K(D)是A^(2)β上的紧算子空间,β为正规权,用β∈R表示,Hilbert空间A^(2)β是L^(2)β的闭子空间,利用Toeplitz算子与紧算子集的距离以及本性范数的定义,得到了非紧Toeplitz算子本性范数的逼近公式。This paper is divided into two parts.The first part studies the Toeplitz operator with L(H)-valued positive operator-valued function G(z)zas symbols on the vector-valued Doubling Fock spaces F2ϕin C,in whichϕis a subharmonic function and dν=ΔϕdA is a non-zero Doubling measure,Δϕ≃1/ρ^(2),through the meet Carleson condition and disappear Carleson several equivalent characterizations,and depicts Carleson conditions,the several equivalent conditions for the boundedness and compactness of Toeplitz Operators with L(H)-valued positive operator-valued function G(z)as symbols are obtained.Then the second part studies essential norm of Toeplitz operators with symbol of L∞on the Bergman spaces A^(2)βinduced by regular-weight on unit disk D,the essential norm of the operator A is defined as||A||e=inf_(B∈K(D)){A-B},K(D)is a compact operator space on A^(2)β,βis a normal weight,expressed byβ∈R,Hilbert space A^(2)βis closed subspace of L^(2)β,and obtains the approximate formula of the essential norm of non-compact Toeplitz operator by using the distance between Toeplitz operators and compact subset and the definition of essential norm.

关 键 词：向量值DoublingFock空间 正规权Bergman空间 TOEPLITZ算子 有界性 本性范数 

分 类 号：TB115[理学—数学]