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In the present note, provided $T\in\mathscr{L(H)}$ is biquasitriangular and Browder's theorem hold for $T$, we show that the spectrum $\sigma$ is continuous at $T$ if and only if the essential spectrum $\sigma_{e}$ is continuous at $T$.
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참고문헌 (12)
참고문헌 신청
B. P. Duggal / 2010 / Continuity of the spectrum on a class of upper triangular operator matrices / Jour. Math. Anal. Appl 370 : 584 ~ 587
C. Apostol / 1973 / Some results on non-quasitriangular operators. IV / Rev. Roum. Math. Pures Appl 18 : 487 ~ 514
I. S. Hwang / 2000 / The spectrum is continuous on the set of phyponormal operators / Math. Z 235 : 151 ~ 157
J. B. Conway / 1979 / Operators that are points of spectral continuity / Integral equations and operator theory 2 : 174 ~ 198
J. B. Conway / 1981 / Operators that are points of spectral continuity II / Integral equations and operator theory 4 : 459 ~ 503
C. Apostol / 1973 / Some results on non-quasitriangular operators. IV / Rev. Roum. Math. Pures Appl 18 : 487 ~ 514
I. S. Hwang / 2000 / The spectrum is continuous on the set of phyponormal operators / Math. Z 235 : 151 ~ 157
J. B. Conway / 1979 / Operators that are points of spectral continuity / Integral equations and operator theory 2 : 174 ~ 198
J. B. Conway / 1981 / Operators that are points of spectral continuity II / Integral equations and operator theory 4 : 459 ~ 503
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