Asymptotic Toeplitz and Hankel operators on the Bergman space

被引：0
作者：
Namita Das
机构：
[1] Utkal University,P.G. Department of Mathematics
来源：
Indian Journal of Pure and Applied Mathematics | 2010年 / 41卷
关键词：
Toeplitz operators; Hankel operators; Bergman space; Hardy space; Bergman shift operator;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper the concept of asymptotic Toeplitz and asymptotic Hankel operators on the Bergman space are introduced and properties of these classes of operators are studied. The importance of this notion is that it associates with a class of operators a Toeplitz operator and with a class of operators a Hankel operator where the original operators are not even Toeplitz or Hankel. Thus it is possible to assign a symbol to an operator that is not Toeplitz or Hankel and hence a symbol calculus is obtained. Further a relation between Toeplitz operators and little Hankel operators on the Bergman space is established in some asymptotic sense.
引用
收藏
页码：379 / 400
页数：21
相关论文
共 11 条
[1]  
Arveson W.(1975)Interpolation problems in nest algebras J. Funct. Anal. 20 208-233
[2]  
Axler S.(1991)Commuting Toeplitz operators with harmonic symbols Integral Equations and Operator Theory 14 1-11
[3]  
Ćućkovic S.(1988)Bergman spaces and their operators, Surveys of some recent results in operator theory (J. B. Conway and B. B. Morrel, editors) Pitman Research Notes in Math. 171 1-50
[4]  
Axler J.(1982)Asymptotic Toeplitz operators Trans. Amer. Math. Soc. 273 621-630
[5]  
Barria P. R.(1992)Density of algebras generated by Toeplitz operators on Bergman spaces Arkiv for Matematik 30 227-243
[6]  
Halmos M.(1989)On asymptotic Toeplitz and Hankel operators Operator Theory: Adv. Appl. 41 241-254
[7]  
Engliś A.(1990)On Hankel operators associated with a class of Non-Toeplitz operators J. Funct. Anal. 94 1-13
[8]  
Feintuch A.(1979)Toeplitz operators on the disc Indiana Univ. Math. J. 28 595-611
[9]  
Feintuch G.(undefined)undefined undefined undefined undefined-undefined
[10]  
McDonald C.(undefined)undefined undefined undefined undefined-undefined
12