Hilbert-Schmidt框架的一些新的不等式

Some New Inequalities for Hilbert-Schmidt Frames

本文利用由两个Hilbert-Schmidt Bessel序列生成的有界线性算子和参数λ∈R构建了Hilbert-Schmidt框架的一些新的不等式.事实表明,当选取恰当的Hilbert-Schmidt Bessel序列和参数λ时,已有的一些关于这个主题的结果可由本文结果推导得到.此外,本文还给出了Hilbert—Schmidt框架的与已有框架不等式相比具有新的结构的三角不等式.

By using a bounded linear operator deriving from two Hilbert–Schmidt Bessel sequences and a parameterλ∈R,we establish several new inequalities for Hilbert–Schmidt frames.It is indicated that some known results on this topic can be obtained when choosing suitable Hilbert–Schmidt Bessel sequences and the parameterλ.We also present some triangle inequalities for Hilbert–Schmidt frames,which possess new structures comparing to previous frame inequalities.