广义Banach框架及其稳定性①

于加东 冯增哲 李海霞

摘 要：本文引入了广义Banach框架的概念，研究了该框架所对应的框架算子的特点，利用框架算子给出了一个广义Banach框架判定的充要条件。并且对该框架穩定性进行了研究，推广了Hilbert空间中的广义框架与可测空间上定义的（Ω，μ）框架稳定性的有关结论。

关键词：广义Banach框架 框架算子 稳定性

中图分类号：O177.1 文献标识码：A 文章编号：1673-9795（2014）05（b）-0193-02

Generalized frames in Banach space and its stability

Yu Jiadong Feng Zengzhe Li Haixia

（College of information and Engineerring of TaiShan medical University，TaiAn，Shandong，271000 China）

Abstract：In this paper，we introduce the conception of Generalized frames in Banach space and study the proprety of the frame operator.A necessary and sufficient condition for Generalized frames is given.Besides，we study the stability of Generalized frames in Banach space and the results of Generalized frames in Hilbert space and （Ω，μ） frames in a measurable space are generalized.

Key Words：Generalized Frames in Banach Space；Frame Operator；Stability