On the circular numerical range of 5-by-5 partial isometries

Authors

  • M. Benharrat Ecole Nationale Polytechnique d’Oran-Maurice Audin (Ex. ENSET d’Oran), Algerie
  • M. Naimi Ecole Nationale Polytechnique d’Oran-Maurice Audin (Ex. ENSET d’Oran), Algerie

DOI:

https://doi.org/10.31926/but.mif.2023.3.65.1.5

Keywords:

numerical range, partial isometric, Sn operators

Abstract

We prove, in some cases in terms of kippenhahn curve, that if 5-by-5 partial isometry whose numerical range is a circular disc then its center must be the origin. This gives a partial affirmative answer to Conjecture 5.1. of [H. l. Gau et al., Linear and Multilinear Algebra, 64 (1) 2016, 14–35.], for the five-dimensional case.

Author Biographies

M. Benharrat, Ecole Nationale Polytechnique d’Oran-Maurice Audin (Ex. ENSET d’Oran), Algerie

BP 1523 Oran-El M’naouar, 31000 Oran

M. Naimi, Ecole Nationale Polytechnique d’Oran-Maurice Audin (Ex. ENSET d’Oran), Algerie

BP 1523 Oran-El M’naouar, 31000 Oran

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Published

2023-07-03

Issue

Vol. 3(65) No. 1 (2023)

Section

MATHEMATICS