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

• Autorzy: Vladimír Müller
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A13: Several-variable operator theory (spectral, Fredholm, etc.)
• 47A12: Numerical range, numerical radius

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 197
• Numer: 3
• Strony: 275-290

Daty

wydano

2010

Twórcy

autor

Vladimír Müller

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

Identyfikatory

DOI

10.4064/sm197-3-5