Hilbert空间中Bessel列的算子扰动  

Operator perturbations of Bessel sequences in a Hilbert space

作　　者：刘琴[1] 曹怀信[1] 王秋芬[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《宝鸡文理学院学报（自然科学版）》2009年第4期1-3,共3页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10571113;10871224)

摘　　要：目的研究Hilbert空间中Bessel列的算子扰动。方法运用算子理论。结果对于Hilbert空间H中的一个序列f={fi}i∞=1及算子列{Tj(i)}i∞,j=1B(H,K),给出使得{∑∞j=1Tj(i)fj}i∞=1成为K中的Bessel序列的一些充分条件;证明了如果{Ti}i∞=1B(H,K)使得Ti=T(i>N0)且f={fi}i∞=1是H中的Bessel列,则{Tifi}i∞=1是K中的Bessel列。结论在一定的条件下,Hilbert空间中的Bessel列经过算子扰动,还可以是Bessel列。Aim Some operator perturbations of Bessel sequences in a Hilbert space were discussed. Methods The operator theory was used. Results For a sequence f={fi}i=1^∞ in a Hilbert space H and an operator sequence {{Tj^（i））i,j=1^∞ belong to B（H,K）, some sufficient conditions for the sequence {∞∑j=1 Tj^（i）fj）i=1^∞ to be a Bessel sequence in K are given. It is proved that the sequence {Tifi}i=1^∞ is a Bessel sequence in K if a sequence {Ti}i=1^∞ belong to B（H,K） can make Ti = Tfor all i 〉 N0 and f = {fi}i=1^∞ is a Bessel sequence in H. Conclusion A Bessel sequence in a Hilbert space after operator perturbation can still be a Bessel sequence under certain conditions.

关 键 词：算子扰动 BESSEL列 HILBERT空间 

分 类 号：O177.1[理学—数学]