编排p-框架和编排q-Riesz基

Weaving p-frames and weaving q-Riesz bases

作为Hilbert空间上编排框架和编排Riesz基的推广,本文研究Banach空间上编排p-框架和编排q-Riesz基.两个p-框架{x_n~*}_(n=1)~∞和{y_n~*}_(n=1)~∞称为是可编排的,如果存在常数0<A≤B<+∞,使得对N的任意子集σ,序列{x_n~*}_(n∈σ)∪{y_n~*}_(n∈σ~c)是一个p-框架且有p-框架界A和B.每个序列{x_n~*}_(n∈σ)∪{y_n~*}_(n∈σ~c)称为一个编排.可编排的q-Riesz基具有类似的定义.本文证明Banach空间上的两个p-框架是可编排的当且仅当它们的每个编排是个p-框架,考虑对偶空间中两个q-Riesz基的可编排性,即借助q-Riesz序列和p-框架的性质给出两个q-Riesz基的每个编排均是q-Riesz基的条件,借助子空间距离的概念给出两个q-Riesz基可编排的几何特征.此外,本文还考虑编排p-框架和编排q-Riesz基的摄动,如小摄动和算子摄动.

As a generalization of weaving frames and weaving Riesz bases in Hilbert spaces, we study weaving p-frames and weaving q-Riesz bases in Banach spaces. Two p-frames {x_n~＊}_（n=1） ~∞and {y_n~＊}_（n=1）~∞are called woven if there exist constants 0 〈A≤B 〈＋∞ such that for every subset σ ？ N, the sequence {x_n~＊}_（n∈σ） ∪ {y_n~＊}_（n∈σ~c） is a p-frame with p-frame bounds A, B. Each sequence {x_n~＊}_（n∈σ） ∪ {y_n~＊}_（n∈σ~c） is called a weaving. The woven q-Riesz bases have similar definitions. We show that two p-frames are woven if every weaving of them is a pframe in Banach spaces. We classify when two q-Riesz bases can be woven in the dual spaces. We give two conditions that every weaving of two q-Riesz bases is a q-Riesz basis in terms of q-Riesz sequences and p-frames,and give a geometric characterization of woven q-Riesz bases in terms of distances between subspaces. Finally,we consider the perturbations of weaving p-frames and weaving q-Riesz bases, such as small perturbations and operator perturbations.