| Banach空间中的X_d框架与Reisz基 |
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| 引用本文： | 李春艳,曹怀信.Banach空间中的X_d框架与Reisz基[J].数学学报,2006,49(6):1361-136. |
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| 作者姓名： | 李春艳 曹怀信 |
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| 作者单位： | [1]陕西师范大学数学与信息科学学院,西安710062 [2]重庆科技学院数理系,重庆400042 |
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| 基金项目： | 国家自然科学基金资助项目（10571113,19771056）;陕西省自然科学研究计划项目（2002A02） |
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| 摘 要： | 本文引入并研究了Banach空间中的X_d框架,X_d Bessel列,紧X_d框架,独立X_d框架和X_d Riesz基等概念,给出了X_d框架和独立X_d框架的算子等价刻画,Banach空间X中存在X_d框架或X_d Riesz基的充要条件以及X_d框架的对偶框架存在的充要条件,讨论了Banach空间的基和X_d框架,X_d Riesz基之间的关系．
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| 关 键 词： | Banach空间 X_d框架 X_d Riesz基 |
| 文章编号： | 0583-1431（2006）06-1361-06 |
| 收稿时间： | 2005-06-15 |
| 修稿时间： | 2005-06-152005-09-30 |
X_d Frames and Reisz Bases for a Banach Space |
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| Chun Yan LI College of Mathematics and Information Science,Shaanxi Normal University,Xi'an ,P.R.China.X_d Frames and Reisz Bases for a Banach Space[J].Acta Mathematica Sinica,2006,49(6):1361-136. |
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| Authors: | Chun Yan LI College of Mathematics and Information Science Shaanxi Normal University Xi'an PRChina |
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| Institution: | Chun Yan LI College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062,P.R.China Department of Mathematics and Physics,Chongqing University of Science and Technology,Chongqing 400042,P.R.China Huai Xin CAO College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062,P.R.China |
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| Abstract: | In this paper, we introduce and discuss Xd frames, Xd Bessel sequences, tight Xd frames, independent Xd frames and Xd Riesz basis for a Banach space. We give a necessary and sufficent condition for a Banach space X to have an Xd frame or to have an Xd Riesz basis, and a necessary and sufficent condition for an Xd frame to have a dual frame. We also discuss some relations among basis, Xd frame and Xd Riesz basis in a Banach space. |
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| Keywords: | Banach space Xd frame Xd Riesz basis |
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