[PDF][PDF] Continuity of approximate point spectrum on the algebra B (X)
S Sánchez-Perales… - Commun. Korean Math …, 2013 - researchgate.net
S Sánchez-Perales, VA Cruz-Barriguete
Commun. Korean Math. Soc, 2013•researchgate.netIn this paper we provide a brief introduction to the continuity of approximate point spectrum
on the algebra B (X), using basic properties of Fredholm operators and the SVEP condition.
Also, we give an example showing that in general it not holds that if the spectrum is
continuous an operator T, then for each λ∈ σs− F (T)\ρ±s− F (T) and ϵ> 0, the ball B (λ, ϵ)
contains a component of σs− F (T), contrary to what has been announced in [JB Conway and
BB Morrel, Operators that are points of spectral continuity II, Integral Equations Operator …
on the algebra B (X), using basic properties of Fredholm operators and the SVEP condition.
Also, we give an example showing that in general it not holds that if the spectrum is
continuous an operator T, then for each λ∈ σs− F (T)\ρ±s− F (T) and ϵ> 0, the ball B (λ, ϵ)
contains a component of σs− F (T), contrary to what has been announced in [JB Conway and
BB Morrel, Operators that are points of spectral continuity II, Integral Equations Operator …
Abstract
In this paper we provide a brief introduction to the continuity of approximate point spectrum on the algebra B (X), using basic properties of Fredholm operators and the SVEP condition. Also, we give an example showing that in general it not holds that if the spectrum is continuous an operator T, then for each λ∈ σs− F (T)\ρ±s− F (T) and ϵ> 0, the ball B (λ, ϵ) contains a component of σs− F (T), contrary to what has been announced in [JB Conway and BB Morrel, Operators that are points of spectral continuity II, Integral Equations Operator Theory 4 (1981), 459–503] page 462.
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