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In this paper we provide a brief introduction to the conti-nuity of approximate point spectrum on the algebra B(X), using basicproperties of Fredholm operators and the SVEP condition. Also, we givean example showing that in general it not holds that if the spectrum iscontinuous an operator T, then for each λ ∈ σs−F (T)|ρ±s−F (T) and ∈ > 0, the ball B(λ, ∈) contains a component of σs−F (T), contrary towhat has been announced in [J. B. Conway and B. B. Morrel, Opera-tors that are points of spectral continuity II, Integral Equations OperatorTheory 4 (1981), 459–503] page 462.
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참고문헌 (15)
참고문헌 신청
B. P. Duggal / 2010 / Continuity of the spectrum on a class of upper triangular operator matrices / J. Math. Anal. Appl 370 : 584 ~ 587
C. Apostol / 1984 / Approximation of Hilbert space operators. Vol. II / Res. Notes Math 102
J. B. Conway / 1979 / Operators that are points of spectral continuity / Integral Equations Operator Theory 2 (2) : 174 ~ 198
J. B. Conway / 1981 / Operators that are points of spectral continuity. II / Integral Equations Operator Theory 4 (4) : 459 ~ 503
J. D. Newburgh / 1951 / The variation of Spectra / Duke Math. J 18 : 165 ~ 176
C. Apostol / 1984 / Approximation of Hilbert space operators. Vol. II / Res. Notes Math 102
J. B. Conway / 1979 / Operators that are points of spectral continuity / Integral Equations Operator Theory 2 (2) : 174 ~ 198
J. B. Conway / 1981 / Operators that are points of spectral continuity. II / Integral Equations Operator Theory 4 (4) : 459 ~ 503
J. D. Newburgh / 1951 / The variation of Spectra / Duke Math. J 18 : 165 ~ 176
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