加权框架的基本性质及其与框架乘子的关系

The properties of weighted frames and a relationship between weighted frames and frame multipliers

研究了加权框架的基本性质及其与框架乘子的关系.首先给出了加权框架的定义,在此基础上证明了加权框架的一些基本性质:两个加权框架的并仍是加权框架;半正规序列与加权框架的乘积仍是加权框架,并用实例进行了说明.同时给出了加权框架与框架乘子的联系,目的在于将加权框架和算子联系起来,为进一步研究奠定理论基础.

This article firstly introduces the definition of weighted frames and some properties of weighted frames are proved, such as the union of two weighted frames is still a weighted frame; the product of a semi-normalized sequence and a weighted frame is still a weighted frame. Some examples are given. Moreover, a relationship between weighted frames and frame multipliers is discussed. A bridge between weighted frames and multipliers is then built, which will be benefit for the further study.