Hilbert空间上的算子值(p,q)-Bessel乘子

Operator valued(p,q)-Bessel multipliers in Hilbert spaces

在Hilbert空间上引入算子值p-框架和算子值(p,q)-Bessel乘子等概念,重点研究乘子,这里1<p,q<∞且1/p+1/q=1.一个算子值(p,q)-Bessel乘子是由一个算子值p-Bessel序列、一个算子值q-Bessel序列和一个有界数列构成.结果表明:(1)在一定条件下,有界数列分别属于c_(0),l^(1)和l^(2)时,乘子分别是紧算子、迹类算子和Hilbert-Schmidt算子;(2)当算子值q-Bessel序列换成p-Riesz基时,有界数列与乘子之间的对应是一对一的;(3)乘子关于其构成元具有连续依赖性.

This paper introduces the concepts of operator valued p-frames and operator valued(p,q)-Bessel multipliers in Hilbert spaces,and the multipliers are mainly studied,where 1<p,q<∞and 1/p+1/q=1.An operator valued(p,q)-Bessel multiplier is determined by an operator valued p-Bessel sequence,an operator valued q-Bessel sequence and a bounded scalar-sequence.The main results of this paper are as follows:(1)Under some conditions,when the bounded scalar-sequence belongs to c_(0),l^(1) and l^(2) respectively,the multiplier is a compact operator,a trace class operator and a Hilbert-Schmidt operator respectively;(2)If the operator valued q-Bessel sequence is replaced by an operator valued p-Riesz basis,then the correspondence between the bounded scalar-sequences and multipliers is one-to-one;(3)The multiplier depends continuously on its component elements.