廣義Banach框架及其穩定性①

于加東 馮增哲 李海霞

摘 要：本文引入了廣義Banach框架的概念，研究了該框架所對應的框架算子的特點，利用框架算子給出了一個廣義Banach框架判定的充要條件。并且對該框架穩定性進行了研究，推廣了Hilbert空間中的廣義框架與可測空間上定義的（Ω，μ）框架穩定性的有關結論。

關鍵詞：廣義Banach框架 框架算子 穩定性

中圖分類號：O177.1 文獻標識碼：A 文章編號：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