Geodesic
The joint essential numerical range, compact perturbations, and the Olsen problem
Vladimír Müller1
1 Mathematical Institute Czech Academy of Sciences Žitna 25, 115 67 Praha 1, Czech Republic
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.
DOI : 10.4064/sm197-3-5
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

Vladimír Müller 1

1 Mathematical Institute Czech Academy of Sciences Žitna 25, 115 67 Praha 1, Czech Republic 
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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

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