Equalities and Inequalities for Norms of Block Imaginary Circulant Operator Matrices

Abstract

Circulant, block circulant-type matrices and operator norms have become effective tools in solving networked systems. In this paper, the block imaginary circulant operator matrices are discussed. By utilizing the special structure of such matrices, several norm equalities and inequalities are presented. The norm $\tau$ in consideration is the weakly unitarily invariant norm, which satisfies $\tau \left(\mathcal{A}\right)=\tau (U\mathcal{A}V)$. The usual operator norm and Schatten $p$-norm are included. Furthermore, some special cases and examples are given.