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

2021/08/10 by Naimi, Mehdi, Benharrat, Mohammed
#FOS: Mathematics #Functional Analysis (math.FA) #Kippenhahn curve #Numerical range #Operator Algebras (math.OA) #Partial isometric

paper · doi:10.48550/arxiv.2108.04459

Abstract

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

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