Let T₁,...,Tₙ be bounded linear operators on a complex Hilbert space H. Then there are compact operators K₁,...,Kₙ ∈ B(H) such that the closure of the joint numerical range of the n-tuple (T₁-K₁,...,Tₙ-Kₙ) equals the joint essential numerical range of (T₁,...,Tₙ). This generalizes the corresponding result for n = 1. We also show that if S ∈ B(H) and n ∈ ℕ then there exists a compact operator K ∈ B(H) such that . This generalizes results of C. L. Olsen.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-3-5,
author = {Vladim\'\i r M\"uller},
title = {The joint essential numerical range, compact perturbations, and the Olsen problem},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {275-290},
zbl = {1193.47007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-3-5}
}
Vladimír Müller. The joint essential numerical range, compact perturbations, and the Olsen problem. Studia Mathematica, Tome 196 (2010) pp. 275-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-3-5/