论文标题
使用融合帧的操作员代表
Representation of Operators Using Fusion Frames
论文作者
论文摘要
为了在许多应用中找到操作方程的数值解，需要在子空间中的分解。因此，有必要将已知的矩阵表示方法扩展到融合帧的利用率。在本文中，我们研究了运营商在Hilbert Space $ \ hil $上的这种表示，并带有Bessel Fusion序列，融合框架和Riesz分解。我们将提供基本定义。我们将显示一些结构性结果并提供一些例子。此外，在Riesz分解的情况下，我们证明这些功能是同构。另外，我们希望找到此类矩阵表示形式的伪内和逆（如果存在）。我们将把这个想法应用于Schatten $ p $ class运营商。最后，我们表明，融合框架的张量是希尔伯特 - 雪橇运营商空间中的框架。
For finding the numerical solution of operator equations in many applications a decomposition in subspaces is needed. Therefore, it is necessary to extend the known method of matrix representation to the utilization of fusion frames. In this paper we investigate this representation of operators on a Hilbert space $\Hil$ with Bessel fusion sequences, fusion frame and Riesz decompositions. We will give the basic definitions. We will show some structural results and give some examples. Furthermore, in the case of Riesz decompositions, we prove that those functions are isomorphisms. Also, we want to find the pseudo-inverse and the inverse (if there exists) of such matrix representations. We are going to apply this idea to the Schatten $p$-class operators. Finally, we show that tensors of fusion frame are frames in the space of Hilbert-Schmidt operators.
