Equalities and inequalities for norms of block imaginary circulant operator matrices. (English) Zbl 1383.15016

Summary: 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 \(\tau (\mathcal{A})= \tau (U \mathcal{A} V)\). The usual operator norm and Schatten \(p\)-norm are included. Furthermore, some special cases and examples are given.


15A42 Inequalities involving eigenvalues and eigenvectors
15B05 Toeplitz, Cauchy, and related matrices
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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