Some facts from descriptive set theory concerning essential spectra and applications

Khalid Latrach, J. Martin Paoli, and Pierre Simonnet. "Some facts from descriptive set theory concerning essential spectra and applications." Studia Mathematica 171.3 (2005): 207-225. <http://eudml.org/doc/284615>.

@article{KhalidLatrach2005,
abstract = {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.},
author = {Khalid Latrach, J. Martin Paoli, Pierre Simonnet},
journal = {Studia Mathematica},
keywords = {essential spectra; Borel maps; strictly singular operators; Fredholm operators; Riesz operators; strongly continuous semigroups; hereditarily indecomposable Banach spaces},
language = {eng},
number = {3},
pages = {207-225},
title = {Some facts from descriptive set theory concerning essential spectra and applications},
url = {http://eudml.org/doc/284615},
volume = {171},
year = {2005},
}

TY - JOUR
AU - Khalid Latrach
AU - J. Martin Paoli
AU - Pierre Simonnet
TI - Some facts from descriptive set theory concerning essential spectra and applications
JO - Studia Mathematica
PY - 2005
VL - 171
IS - 3
SP - 207
EP - 225
AB - 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.
LA - eng
KW - essential spectra; Borel maps; strictly singular operators; Fredholm operators; Riesz operators; strongly continuous semigroups; hereditarily indecomposable Banach spaces
UR - http://eudml.org/doc/284615
ER -