[1]杨向东.单位球上加权Banach空间中的Toeplitz算子(英文)[J].江西师范大学学报(自然科学版),2014,(06):557-560.
　YANG Xiang-dong.The Toeplitz Operators on the Weighted Banach Space of the Unit Ball[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(06):557-560.
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单位球上加权Banach空间中的Toeplitz算子(英文)()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2014年06期
页码:
557-560
栏目:
出版日期:
2014-12-31

文章信息/Info

Title:
The Toeplitz Operators on the Weighted Banach Space of the Unit Ball
作者:
杨向东
昆明理工大学数学系,云南 昆明,650093
Author(s):
YANG Xiang-dong
关键词:
Toeplitz算子; 加权Banach空间; 连续性; 紧致性
Keywords:
Toeplitz operators; weighted Banach spaces; continuity; compactness
分类号:
O174.5
文献标志码:
A
摘要:
应用Berezin变换的方法对单位球上加权Banach空间中的 Toeplitz算子进行刻画，对正函数的情形，将现有的单位圆的相关结论推广至单位球，得到Toeplitz算子连续的充分必要条件，并给出Toeplitz算子为紧算子的充分条件。
Abstract:
In the case of positive symbols,the continuity and compactness of a Toeplitz operator are character-ized. The Toeplitz operator under investigation acts upon the weighted Banach space H∞U which consists of analytic functions on the unit ball of Cn . Our characterizations are in terms of the Berezin transform.

参考文献/References:

[1] Zhu Kehe.Positive toeplitz operators on weighted bergman spaces of bounded symmetric domains [J].J Operator Theory,1988,20(2):329-357.
[2] Zhu Kehe.Schatten class toeplitz operators on weighted bergman spaces of the unit ball [J].New York J Math,2007,13:299-316.
[3] Zhu Kehe.Operator theory in function spaces [M].New York:Marcel Dekker,1990.
[4] Berger C A,Coburn L A.Toeplitz operators and quantum mechanics [J].J Funct Anal,1986,68(3):273-299.
[5] Berger C A,Coburn L A.Toeplitz operators on the Segal-Bargmann space [J].Trans Amer Math Soc,1987,301(2):813-829.
[6] Berger C A,Coburn L A.Heat flow and Berezin-Toeplitz estimates [J].Amer J Math,1994,116(3):563-590.
[7] Berger C A,Coburn L A,Zhu Kehe.Toeplitz operators and function theory in n-dimensions [J].Lecture Notes in Math,1987,1256:28-35.
[8] Bonet J,Taskinen J.Toeplitz operators on the space of analytic functions with logarithmic growth [J].J Math Anal Appl,2009,353(1):428-435.
[9] Kothe G.Topological vector spaces I and II [M].Berlin:Springer-Verlag,1979.
[10] Rudin W.Function theory in the unit ball of Cn [M].New York:Springer-Verlag,1980.
[11] Zhu Kehe.Spaces of holomorphic functions in the unit ball [M].New York:Springer-Verlag,2005.

备注/Memo

备注/Memo:
国家自然科学基金(11261024)
更新日期/Last Update: 1900-01-01