Banach空间中的Xd Bessel列

J4 ›› 2011, Vol. 46 ›› Issue (4): 98-102.

Banach空间中的X_d Bessel列

王亚丽,曹怀信,张巧卫

陕西师范大学数学与信息科学学院, 陕西西安710062

收稿日期:2010-01-23 发布日期:2011-04-21
作者简介:王亚丽(1983- ), 女,硕士研究生,主要从事算子理论与小波分析研究. Email:wangyali831220@163.com
基金资助:
国家自然科学基金资助项目(10571113; 10871224); 陕西省自然科学研究计划(2009JM1011)

Sequences of X_dBessel for a Banach space

WANG Ya-li, CAO Huai-xin, ZHANG Qiao-wei

College of Mathematics and Information Sciences, Shaanxi Normal University, Xi′an 710062, Shaanxi, China

Received:2010-01-23 Published:2011-04-21

摘要/Abstract

摘要：

研究了Banach空间X中的X_d Bessel列、X_d框架、X_d独立框架、X_d紧框架与X_dRiesz基。证明了当X_d为BK-空间时, (B^Xd_X,‖·‖)是数域F上的Banach空间;当X_d是BK-空间且X自反时, 通过定义算子T_f, 建立了空间B^Xd_X 与算子空间B(X*,X_d)之间的等距同构, 为利用算子论的方法研究X_d Bessel列提供了必要的理论依据。最后, 给出了Banach空间X中X_d Bessel列的等价刻画并证明了独立的X_d 框架与X_d Riesz基是一致的。

关键词: X_d Bessel列; X_d框架; X_d Riesz基

Abstract:

Xd Bessel sequences, X_d frames, X_d independent frames, X_d tight frames and X_dRiesz basis for a Banach space X are introduced and discussed. It is proved that (B^Xd_X,‖·‖) is a Banach space when X_d is a BK-space. By defining an operator Tf, an isometric isomorphism from B^Xd_Xto B(X*,X_d) is established when X_dis 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 X_dBessel sequences for a Banach space X are given. Also, it is proved that independent X_d frames and X_d Riesz bases for a Banach space X are the same.

Key words: X_dBessel sequence; X_dframe; X_d Riesz basis

王亚丽,曹怀信,张巧卫. Banach空间中的X_d Bessel列[J]. J4, 2011, 46(4): 98-102.

WANG Ya-li, CAO Huai-xin, ZHANG Qiao-wei. Sequences of X_dBessel for a Banach space[J]. J4, 2011, 46(4): 98-102.

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