The joint essential numerical range, compact perturbations,
and the Olsen problem
Studia Mathematica, Tome 197 (2010) no. 3, pp. 275-290
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $T_1,\ldots,T_n$ be bounded linear operators on a complex Hilbert space $H$. Then there are compact operators $K_1,\dots,K_n\in B(H)$ such that the closure of the joint numerical range of the $n$-tuple $(T_1-K_1,\ldots,T_n-K_n)$ equals the joint essential numerical range of $(T_1,\ldots,T_n)$. This generalizes the corresponding result for $n=1$.We also show that if $S\in B(H)$ and $n\in\mathbb N$ then there exists a compact operator $K\in B(H)$ such that $\|(S-K)^n\|=\|S^n\|_e$. This generalizes results of C. L. Olsen.
Keywords:
ldots bounded linear operators complex hilbert space there compact operators dots closure joint numerical range n tuple k ldots n k equals joint essential numerical range ldots generalizes corresponding result mathbb there exists compact operator s k generalizes results olsen
Affiliations des auteurs :
Vladimír Müller 1
Vladimír Müller. The joint essential numerical range, compact perturbations, and the Olsen problem. Studia Mathematica, Tome 197 (2010) no. 3, pp. 275-290. doi: 10.4064/sm197-3-5
@article{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},
pages = {275--290},
year = {2010},
volume = {197},
number = {3},
doi = {10.4064/sm197-3-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm197-3-5/}
}
TY - JOUR AU - Vladimír Müller TI - The joint essential numerical range, compact perturbations, and the Olsen problem JO - Studia Mathematica PY - 2010 SP - 275 EP - 290 VL - 197 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4064/sm197-3-5/ DO - 10.4064/sm197-3-5 LA - en ID - 10_4064_sm197_3_5 ER -
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