Banach空间中p阶Bessel列的扰动  

Perturbations of Bessel Sequences of Order p in a Banach Space

作　　者：王秋芬[1,2] 曹怀信[2] 武海辉[1] 

机构地区：[1]安康学院数学系,陕西安康7250001 [2]陕西师范大学数学与信息科学学院,西安710062

出　　处：《吉林大学学报（理学版）》2011年第3期397-404,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:1057111310871224);陕西省自然科学研究计划项目(批准号:2009JM1011)

摘　　要：应用算子论方法研究Banach空间X中p(1<p<∞)阶Bessel列的扰动问题,对X中的任一p阶Bessel列f={fi}i∈I,定义了有界线性算子Tf:X*→lp,建立了从全体p阶Bessel列组成的Banach空间BpX(I)到算子空间B(X*,lp)上的等距线性同构α:f→Tf,并给出了p阶Bessel列的扰动定理.With the aid of operator theory,some perturbations of Bessel sequences of order p in a Banach space X were discussed.For a Bessel sequence f={fi}i∈I of order p in X,we defined a bounded linear operator Tf from X＊ into lp and established a linear isometry isomorphism α from the space BpX（I） of all the Bessel sequences of order p in a Banach space X into the operator space B（X＊,lp） defined by α（f）=Tf.In the light of operator theory,some results on perturbations of Bessel sequences of order p were given,which are helpful to the study of frames of order p for a Banach space.

关 键 词：扰动 p阶Bessel列 BANACH空间 

分 类 号：O177.1[理学—数学]