分块对称r循环算子的范数不等式  

Norm Inequalities for Block Symmetric r-Circulant Operator

作　　者：史一彬 秦梅[1] 

机构地区：[1]上海理工大学理学院

出　　处：《上海理工大学学报》2019年第6期511-515,共5页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目（11601332）;沪江基金资助项目（B14005）

摘　　要：循环(块循环)算子是一类重要的算子,在量子计算、时间序列分析、压缩感知等科学与工程计算中有着广泛的应用。分块对称r循环(r反循环)算子的生成方式可以看作是将循环算子的生成方式取对称,并将副对角线以下的元素添加参数r或-r,r>0。基于降阶思想,利用分块对称r循环矩阵的对角化性质和酉不变(弱酉不变)范数的性质,给出了分块对称r循环算子和分块对称r反循环算子由子块导出的算子范数和Schatten p–范数不等式和等式结果。Circulant(block circulant) operators are an important class of operators, which have wide applications in science and engineering calculations such as quantum computation, time-series analysis and compressing sensing, etc. The generation of block symmetric r-circulant operators(block symmetric r-skew-circulant operators) can be seen as symmetrical generation of circulant operators and adding parameters r or-r to entries below the para-diagonal elements. Based on the idea of order reduction, and using the properties of the diagonalization of block symmetric r-circulant operator matrices and unitarily invariant(weakly unitarily invariant) norm, the operator norms and Schatten p-norm inequalities and equality results of the block symmetric r-circulant operators and the block symmetric r-skew-circulant operators derived from the sub-block are given.

关 键 词：分块对称r循环算子 分块对称r反循环算子 酉不变范数 算子范数 Schattenp–范数 不等式 

分 类 号：O151.2[理学—数学]