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Positivity

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Positive semidefinite indicator property for norm-numerical range

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Abstract

In this paper, using an elementary method, we prove that if norm-numerical range related to an absolute norm \(\Vert .\Vert \) on \(\mathbb {C}^n\) satisfies the positive semidefinite indicator property, then \(\Vert .\Vert \) will be a multiple of Euclidian norm.

Keywords

Matrix analysis Numerical range Bauer numerical range 

Mathematics Subject Classification

15A60 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsShahed UniversityTehranIran

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