The joint essential numerical range, compact perturbations, and the Olsen problem

Vladimír Müller. "The joint essential numerical range, compact perturbations, and the Olsen problem." Studia Mathematica 197.3 (2010): 275-290. <http://eudml.org/doc/285408>.

@article{VladimírMüller2010,
abstract = {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 $||(S-K)ⁿ|| = ||Sⁿ||_\{e\}$. This generalizes results of C. L. Olsen.},
author = {Vladimír Müller},
journal = {Studia Mathematica},
keywords = {joint numerical range; joint essential numerical range; compact perturbation; Olsen's problem},
language = {eng},
number = {3},
pages = {275-290},
title = {The joint essential numerical range, compact perturbations, and the Olsen problem},
url = {http://eudml.org/doc/285408},
volume = {197},
year = {2010},
}

TY - JOUR
AU - Vladimír Müller
TI - The joint essential numerical range, compact perturbations, and the Olsen problem
JO - Studia Mathematica
PY - 2010
VL - 197
IS - 3
SP - 275
EP - 290
AB - 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 $||(S-K)ⁿ|| = ||Sⁿ||_{e}$. This generalizes results of C. L. Olsen.
LA - eng
KW - joint numerical range; joint essential numerical range; compact perturbation; Olsen's problem
UR - http://eudml.org/doc/285408
ER -