乘子的无条件收敛与可逆性
泛函分析
2012-06-15 v3
摘要
本文研究了乘子的无条件收敛与可逆性。乘子是由（类框架）分析、乘以固定符号以及再合成所产生的算子。根据分析序列与合成序列以及符号的性质，确定了无条件收敛与可逆性的充分和/或必要条件。给出的例子表明，所给的断言涵盖了不同类别的乘子。如果乘子是可逆的，则确定了其逆算子的公式。其中一个序列为 Riesz 基的情况得到了完全刻画。
引用
@article{arxiv.0911.2783,
title = {Unconditional convergence and invertibility of multipliers},
author = {D. Stoeva and P. Balazs},
journal= {arXiv preprint arXiv:0911.2783},
year = {2012}
}
备注
31 pages; changes to previous version: 1.) the results from the previous version are extended to the case of complex symbols m. 2.) new statements about the unconditional convergence and boundedness are added (3.1,3.2 and 3.3). 3.) the proof of a preliminary result (Prop. 2.2) was moved to a conference proceedings [29]. 4.) Theorem 4.10. became more detailed