Some facts from descriptive set theory concerning essential spectra and applications

• Autorzy: Khalid Latrach , J. Martin Paoli , Pierre Simonnet
• Języki publikacji: EN

Abstrakty

EN

Let X be a separable Banach space and denote by 𝓛(X) (resp. 𝒦(ℂ)) the set of all bounded linear operators on X (resp. the set of all compact subsets of ℂ). We show that the maps from 𝓛(X) into 𝒦(ℂ) which assign to each element of 𝓛(X) its spectrum, approximate point spectrum, essential spectrum, Weyl essential spectrum, Browder essential spectrum, respectively, are Borel maps, where 𝓛(X) (resp. 𝒦(ℂ)) is endowed with the strong operator topology (resp. Hausdorff topology). This enables us to derive the topological complexity of some subsets of 𝓛(X) and to discuss the properties of a class of strongly continuous semigroups. We close the paper by giving a characterization of strongly continuous semigroups on hereditarily indecomposable Banach spaces.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 47D03: Groups and semigroups of linear operators
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 171
• Numer: 3
• Strony: 207-225

Daty

wydano

2005

Twórcy

autor

Khalid Latrach

• Laboratoire de Mathématiques, CNRS (UMR 6620), Université Blaise Pascal, 24 avenue des Landais, 63117 Aubière, France

autor

J. Martin Paoli

• Département de Mathématiques, Université de Corse, Quartier Grossetti, BP 52, 20250 Corte, France

autor

Pierre Simonnet

• Département de Mathématiques, Université de Corse, Quartier Grossetti, BP 52, 20250 Corte, France

Identyfikatory

DOI

10.4064/sm171-3-1