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M-numerical ranges of odd-order tensors based on operators

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Abstract

In this paper, we use tensor norm to define M-numerical ranges of odd-order tensors. This notion of numerical range can be useful in the design of fast algorithms for the computation of tensor eigenvalues. Also, we introduce normal tensors based on a product for odd-order tensors. The basic properties of the numerical range of a matrix, such as compactness and convexity, are proved to hold for the M-numerical range of an odd-order tensor. We find the M-numerical range of a normal tensor. Next, we introduce the singular-value decomposition of an odd-order tensor (\(T_M\)-SVD), and then use it to find the M-numerical range of the tensor.

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Authors and Affiliations

  1. Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

    Mehri Pakmanesh & Hamidreza Afshin

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  1. Mehri Pakmanesh
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  2. Hamidreza Afshin
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Communicated by Qing-Wen Wang.

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Pakmanesh, M., Afshin, H. M-numerical ranges of odd-order tensors based on operators. Ann. Funct. Anal. 13, 37 (2022). https://doi.org/10.1007/s43034-022-00183-8

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  • DOI: https://doi.org/10.1007/s43034-022-00183-8

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