Abstract
This paper deals with general \({n\times n}\) upper-triangular operator matrices with given diagonal entries. The characterizations of perturbations of their point spectra, residual spectra and continuous spectra are given, based on the space decomposition method.
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References
Barnes B.A.: Riesz points of upper triangular operator matrices. Proc. Am. Math. Soc. 133, 1343–1347 (2005)
Barraa M., Boumazgour M.: On the perturbations of spectra of upper triangular operator matrices. J. Math. Anal. Appl. 347, 315–322 (2008)
Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, New York (2003)
Cao X.: Browder spectra for upper triangular operator matrices. J. Math. Anal. Appl. 342, 477–484 (2008)
Chen A., Qi Y., Huang J.: Left invertibility of formal Hamiltonian operators. Linear Multilinear Algebra 63, 235–243 (2015)
Djordjević D.S.: Perturbations of spectra of operator matrices. J. Oper. Theory 48, 467–486 (2002)
Du H., Pan J.: Perturbation of spectrums of \({2\times 2}\) operator matrices. Proc. Am. Math. Soc 121, 761–766 (1994)
Djordjević S.V., Zguitti H.: Essential point spectra of operator matrices trough local spectral theory. J. Math. Anal. Appl. 338, 285–291 (2008)
Gohberg I., Goldberg S., Kaashoek M.A.: Classes of Linear Operators. Birkhauser Verlag, Basel (1990)
Huang J., Huang Y., Wang H.: Closed range and Fredholm properties of upper-triangular operator matrices. Ann. Funct. Anal. 6, 42–52 (2015)
Han J.K., Lee H.Y., Lee W.Y.: Invertible completions of \({2\times 2}\) upper triangular operator matrices. Proc. Am. Math. Soc. 128, 119–123 (1999)
Ji Y.: Quasitriangular + small compact = strongly irreducible. Trans. Am. Math. Soc. 351, 4657–4673 (1999)
Lee W.Y.: Weyl spectra of operator matrices. Proc. Am. Math. Soc. 129, 131–138 (2001)
Zguitti H.: A note on Drazin invertibility for upper triangular block operators. Mediterr. J. Math. 10, 1497–1507 (2013)
Zhang S., Wu Z., Zhong H.: Continuous spectrum, point spectrum and residual spectrum of operator matrices. Linear Algebra Appl. 433, 653–661 (2010)
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Huang, J., Wu, X. & Chen, A. The Point Spectrum, Residual Spectrum and Continuous Spectrum of Upper-Triangular Operator Matrices with Given Diagonal Entries. Mediterr. J. Math. 13, 3091–3100 (2016). https://doi.org/10.1007/s00009-015-0673-5
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DOI: https://doi.org/10.1007/s00009-015-0673-5