CONTINUITY OF APPROXIMATE POINT SPECTRUM ON THE ALGEBRA B(X)

Title & Authors
CONTINUITY OF APPROXIMATE POINT SPECTRUM ON THE ALGEBRA B(X)

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 $\small{{\lambda}{\in}{\sigma}_{s-F}(T){\setminus}\overline{{\rho}^{\pm}_{s-F}(T)}}$ and $\small{{\in}}$ > 0, the ball $\small{B({\lambda},{\in})}$ contains a component of $\small{{\sigma}_{s-F}(T)}$, contrary to what has been announced in [J. B. Conway and B. B. Morrel, Operators that are points of spectral continuity II, Integral Equations Operator Theory 4 (1981), 459-503] page 462.
Keywords
approximate point spectrum;continuity of the spectrum;
Language
English
Cited by
1.
WEYL'S THEOREM, TENSOR PRODUCT, FUGLEDE-PUTNAM THEOREM AND CONTINUITY SPECTRUM FOR k-QUASI CLASS An* OPERATO,;;

대한수학회지, 2014. vol.51. 5, pp.1089-1104
1.
WEYL'S THEOREM, TENSOR PRODUCT, FUGLEDE-PUTNAM THEOREM AND CONTINUITY SPECTRUM FOR k-QUASI CLASS An*OPERATO, Journal of the Korean Mathematical Society, 2014, 51, 5, 1089
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