Multipliers for p-Bessel Sequences in Banach Spaces
Multipliers for p-Bessel Sequences in Banach Spaces
复制标题
DOI：
10.1007/s00020-010-1814-7
复制
发表时间：
2010-04
影响因子：
0.8
通讯作者：
A. Rahimi;P. Balázs
中科院分区：
文献类型：
--
作者：
A. Rahimi;P. Balázs
最近，乘法器被引入作为贝塞尔序列和希尔伯特空间中的框架的算子。这些运算符由插入在分析和综合运算符之间的固定乘法模式（符号）定义。在本文中，我们将推广巴纳赫空间中 p-Bessel 和 p-Riesz 序列的贝塞尔乘子的概念。将证明有界符号导致有界运算符。符号收敛到零会产生紧凑算子。此外，我们将为倍增者成为核运营商提供充分的条件。最后，我们将展示乘法器对其参数的连续依赖性。
Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers forp-Bessel andp-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.