Local spectrum and local spectral radius of an operator at a fixed vector

• Autorzy: Janko Bračič , Vladimír Müller
• Języki publikacji: EN

Abstrakty

EN

Let 𝒳 be a complex Banach space and e ∈ 𝒳 a nonzero vector. Then the set of all operators T ∈ ℒ(𝒳) with $σ_{T}(e) = σ_δ(T)$, respectively $r_{T}(e) = r(T)$, is residual. This is an analogy to the well known result for a fixed operator and variable vector. The results are then used to characterize linear mappings preserving the local spectrum (or local spectral radius) at a fixed vector e.

Kategorie tematyczne

• 47B49: Transformers, preservers (operators on spaces of operators)
• 47A11: Local spectral properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 194
• Numer: 2
• Strony: 155-162

Daty

wydano

2009

Twórcy

autor

Janko Bračič

• IMFM, University of Ljubljana, Jadranska ul. 19, SI-1000 Ljubljana, Slovenia

autor

Vladimír Müller

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

Identyfikatory

DOI

10.4064/sm194-2-3