Banach空间上q-Besselian框架的稳定性  

Stability of q-Besselian Frame in Banach Spaces

作　　者：艾瑛[1] 卢立才[2] 

机构地区：[1]沈阳建筑大学理学院,辽宁沈阳110168 [2]沈阳师范大学计算机与数学基础教学部,辽宁沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2010年第1期12-13,共2页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省高等学校科学研究项目(20060792)

摘　　要：人们对框架理论研究的日益广泛和深入,目前对框架的研究已经从Hilbert空间推广到Banach空间,并获得了许多重要结论。首先通过引入分析算子和合成算子的概念,以及q-Besselian框架的等价命题,把Hilbert空间上Besselian框架的稳定性推广到Banach空间,建立Banach空间上q-Besselian框架的合成算子与Fredholm算子之间的联系,得到了q-Besselian框架的充要条件是Fredholm算子的结论。并在此基础上,得出了满足q-Besselian框架的其他结论。文中所得的结论可为研究q-Besselian框架的性质提供了新的视角和方法。People take increasingly indepth research of frame theory, and the current research of frame theory has extended to the Banach space from the Hilbert space. In the mean while, it received a number of important conclusions. To begin with of this paper, it introduced the concept of analysis operator and synthesis operator, equivalent propositions of q-Besselian frame are clarified at the same time, the stability of the Besselian frame theory is extended from the Hilbert space to the Banach spaces, it also get the one-to-one correspondence relation between synthesis operator of q-Besselian frame and Fredholm operator. A condusion that sufficient and necessary conditions of q-Besselian frame is Fredholm operator are also obtained. On this basis, the other conclusion of q-Besselian frame are expounded. The discusssion results can lend to study the properties of the q-Besselian frame and provide a new perspective and methods to continue the research.

关 键 词：q-Besselian框架 FREDHOLM算子 BANACH空间 

分 类 号：O174.2[理学—数学]