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| Banach空间中的Bd Bessel列 | |
| 引用本文： | 王亚丽,曹怀信,张巧卫. Banach空间中的Bd Bessel列[J]. 山东大学学报(自然科学版), 2011, 0(4): 98-102 |
| 作者姓名： | 王亚丽 曹怀信 张巧卫 |
| 作者单位： | 陕西师范大学数学与信息科学学院,陕西西安710062 |
| 摘 要： | 研究了Banach空间X中的Xd Bessel列、Xd框架、Xd独立框架、Xd紧框架与Xd Riesz基。证明了当Xd为BK-空间时,（BXXd,‖·‖）是数域F上的Banach空间;当Xd是BK-空间且X自反时,通过定义算子Tf,建立了空间BXXd与算子空间B（X＊,Xd）之间的等距同构,为利用算子论的方法研究Xd Bessel列提供了必要的理论依据。最后,给出了Banach空间X中Xd Bessel列的等价刻画并证明了独立的Xd框架与Xd Riesz基是一致的。 |
| 关 键 词： | Xd Bessel列 Xd框架 Xd Riesz基 |
Sequences of Xd Bessel for a Banach space |
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| WANG Ya-li,CAO Huai-xin,ZHANG Qiao-wei. Sequences of Xd Bessel for a Banach space[J]. Journal of Shandong University(Natural Science Edition), 2011, 0(4): 98-102 | |
| Authors: | WANG Ya-li CAO Huai-xin ZHANG Qiao-wei |
| Affiliation: | (College of Mathematics and Information Sciences, Shaanxi Normal University, Xi＇an 710062, Shaanxi, China) |
| Abstract: | Xd Bessel sequences, Xd frames, Xd independent frames, Xd tight frames and Xd Riesz basis for a Banach space X are introduced and discussed. It is proved that （BXXd,‖·‖） is a Banach space when Xd is a BK-space. By de- fining an operator TI, an isometric isomorphism from Bxxd to B（X＊,Xd ） is established when Xd is a BK-space and X is reflexive, which provides a necessary theoretical basis for studying Xd Bessel sequences by the operator theory. Finally, the equivalent characterizations of Xd Bessel sequences for a Banach space X are given. Also, it is proved that independ- ent Xd frames and Xd Riesz bases for a Banach space X are the same. |
| Keywords: | Xd Bessel sequence Xd frame Xd Riesz basis |
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