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Norm estimates of ω-circulant operator matrices and isomorphic operators for ω-circulant algebra

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Abstract

An n ×n ω-circulant matrix which has a specific structure is a type of important matrix. Several norm equalities and inequalities are proved for ω-circulant operator matrices with ω = eiθ (0 ≤ θ < 2π) in this paper. We give the special cases for norm equalities and inequalities, such as the usual operator norm and the Schatten p-norms. Pinching type inequality is also proposed for weakly unitarily invariant norms. Meanwhile, we present that the set of ω-circulant matrices with complex entries has an idempotent basis. Based on this basis, we introduce an automorphism on the ω-circulant algebra and then show different operators on linear vector space that are isomorphic to the ω-circulant algebra. The function properties, other idempotent bases and a linear involution are discussed for ω-circulant algebra. These results are closely related to the special structure of ω-circulant matrices.

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Authors and Affiliations

  1. Department of Mathematics, Linyi University, Linyi, 276000, China

    ZhaoLin Jiang & TingTing Xu

  2. School of Mathematical Sciences, Shandong Normal University, Ji’nan, 250014, China

    TingTing Xu

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  1. ZhaoLin Jiang
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  2. TingTing Xu
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Correspondence to TingTing Xu.

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Jiang, Z., Xu, T. Norm estimates of ω-circulant operator matrices and isomorphic operators for ω-circulant algebra. Sci. China Math. 59, 351–366 (2016). https://doi.org/10.1007/s11425-015-5051-z

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  • DOI: https://doi.org/10.1007/s11425-015-5051-z

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