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A note on spectral continuity
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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 $T$.
Abstract
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 $T$.
참고문헌 (12)
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- N. Dunford, "Spectral operators", Paci c J. Math, 4, pp.321~354 (1954)
- S. V. Djordjevic, "Weyl's theorem and continuity of spectra in the class of p-hyponormal operators", Studia Math, 143, pp.23~32 (2000)
- S. V.Djordjevic, "Browder's theorem and spectral continuity", Glasgow Math. J, 42, pp.479~486 (2000)
- S. V.Djordjevic, "Continuity of the essential spectrum in the class of quasihy-ponormal operators", Vesnik Math, 50, pp.71~74 (1998)
- B. P. Duggal, "Continuity of the spectrum on a class of upper triangular operator matrices", Jour. Math. Anal. Appl, 370, pp.584~587 (2010)
- R. Harte, "Another note on Weyl's theorem", Trans. Amer. Math. Soc, 349, pp.2115~2124 (1997)
- I. S. Hwang, "The spectrum is continuous on the set of phyponormal operators", Math. Z, 235, pp.151~157 (2000)
- R. Lange, "Biquasitriangularity and spectral continuity", Glasgow Math. J, 26, pp.177~180 (1985)
- J. D. Newburgh, "The variation of spectra", Duke Math. J, 18, pp.165~176 (1951)
관련 논문AI추천
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