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

Janko Bračič, and Vladimír Müller. "Local spectrum and local spectral radius of an operator at a fixed vector." Studia Mathematica 194.2 (2009): 155-162. <http://eudml.org/doc/286117>.

@article{JankoBračič2009,
abstract = {Let be a complex Banach space and e ∈ a nonzero vector. Then the set of all operators T ∈ ℒ() 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.},
author = {Janko Bračič, Vladimír Müller},
journal = {Studia Mathematica},
keywords = {surjectivity spectrum; local spectrum; spectral radius; local spectral radius; linear maps preserving the local spectrum},
language = {eng},
number = {2},
pages = {155-162},
title = {Local spectrum and local spectral radius of an operator at a fixed vector},
url = {http://eudml.org/doc/286117},
volume = {194},
year = {2009},
}

TY - JOUR
AU - Janko Bračič
AU - Vladimír Müller
TI - Local spectrum and local spectral radius of an operator at a fixed vector
JO - Studia Mathematica
PY - 2009
VL - 194
IS - 2
SP - 155
EP - 162
AB - Let be a complex Banach space and e ∈ a nonzero vector. Then the set of all operators T ∈ ℒ() 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.
LA - eng
KW - surjectivity spectrum; local spectrum; spectral radius; local spectral radius; linear maps preserving the local spectrum
UR - http://eudml.org/doc/286117
ER -