调和Hardy空间上的Toeplitz算子的酉等价性  

The Unitary Equivalence of the Toeplitz Operators on the Harmonic Hardy Space

作　　者：丁宣浩[1,2] 黄雨浩 李永宁 Xuanhao Ding;Yuhao Huang;Yongning Li(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067;Chongqing Key Laboratory of Social Economy and Applied Statistics,Chongqing 400067)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]经济社会应用统计重庆市重点实验室,重庆400067

出　　处：《数学物理学报（A辑）》2023年第1期27-34,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金(11871122,12101092);重庆市自然科学基金(cstc2020jcyj-msxmX0318);重庆工商大学基金(2056008)和重庆工商大学校级科研项目(yjscxx2022-112-73)。

摘　　要：记H_(2)是单位圆盘D={ξ∈C:|ξ|<1}上的经典Hardy空间.设u和v是内函数且至少其中一个是非常值的,调和Hardy空间H_(u,v)^(2)定义为H_(u,v)^(2)=uH_(2)⊕v(H_(2))丄=uH_(2)⊕vzH_(2).对任意的x∈H_(u,v)^(2),定义H_(u,v)^(2)上的调和Toeplitz算子Tφx=Qu,v(φx),其中,Qu,v:L_(2)→H_(u,v)^(2)为正交投影.该文刻画了调和Toeplitz算子和对偶截断Toeplitz算子的酉等价性,并给出了两个调和Toeplitz算子可交换的充要条件,调和Toeplitz代数的性质以及Tz的换位子的刻画.最后,该文还得到了有限多个连续符号的调和Toeplitz算子乘积的本质谱.Let H_(2)be the Hardy space on the unit disk D={ξ∈C:|ξ|<1}.Suppose u and v are inner functions and at least one of them is nonconstant,the harmonic Hardy space Hu,v~2 is defined by H_(u,v)^(2)=uH~2⊕v(H_(2))⊥=uH_(2)⊕vzH_(2).For any x∈H_(u,v)^(2),define the Toeplitz operator on the H_(u,v)^(2)by Tφx=Qu,v(φx)where Qu,vis the orthogonal projection from L_(2)→H_(u,v)^(2).In this paper,the unitary equivalence of the harmonic Toeplitz operator and the dual truncated Toeplitz operator is obtained,moreover,the sufficient and necessary conditions for when two Toeplitz operators commute is given,and the properties of the harmonic Toeplitz algebra and the commutant of Tz are described.Finally,the essential spectrum for the product of finitely many harmonic Toeplitz operators with continuous symbols is obtained in this paper.

关 键 词：调和Hardy空间 调和Toeplitz算子 酉等价 对偶截断Toeplitz算子 本质谱 

分 类 号：O177.1[理学—数学]