Hilbert K-模上广义框架的和与直和的稳定性

Stability of sum and direct sum of generalized frame in Hilbert K-module

引入紧算子代数模(简称Hilbert K-模)上的广义框架的概念,用泛函分析和算子代数的理论知识,并结合广义框架的和与直和的性质,给出Hilbert K-模上广义Bessel序列,广义(正规紧)框架的和与直和的稳定性.

A concept of generalized frame in fastened operator algebra module （Hilbert K-module for short） was introduced. The theory of functional analysis and operator algebras and the properties of sum and direct sum of generalized frame in Hilbert K-modules were used to give the Stability of sum and direct sum of generalized Bessel series or generalized （normalized tightness） frame in Hilbert K-module.