ALGEBRAIC DEGREE IN SPATIAL MATRICIAL NUMERICAL RANGES OF LINEAR OPERATORS

First published in Proceedings of the American Mathematical Society in volume 149, issue 10 in 2021, published by the American Mathematical SocietyWe study the maximal algebraic degree of principal ortho-compressions of linear operators that constitute spatial matricial numerical ranges of higher order. We demonstrate (amongst other things) that for a (possibly unbounded) operator L on a Hilbert space, every principal m-dimensional ortho-compression of L has algebraic degree less than m if and only if rank(L − λI) ≤ m − 2 for some λ ∈ CThe first author’s research was supported in part by Research and Development Agency of Slovenia grant P1-0222. The second author’s research was supported by Colby College Natural Sciences Division Grant. The third, fourth, and fifth authors’ research was supported in part by NSERC (Canada)