Li, Guangfang; Hai, Guojun; Chen, Alatancang Generalized Weyl spectrum of upper triangular operator matrices. (English) Zbl 1321.47008 Mediterr. J. Math. 12, No. 3, 1059-1067 (2015). Summary: Let \(M_C=\left(\begin{smallmatrix} A & C\\ 0 & B\end{smallmatrix}\right)\) be a \(2\times 2\) upper triangular operator matrix on Hilbert space \(\mathcal H\oplus\mathcal K\). For given operators \(A\in\mathcal B(\mathcal H)\) and \(B\in\mathcal B(\mathcal K)\), sets \(\bigcap_{C\in\mathcal B(\mathcal K,\mathcal H)}\sigma^g_w(M_C)\) and \(\bigcup_{C\in\mathcal B(\mathcal K,\mathcal H)}\sigma^g_w(M_C)\) are investigated, where \(\sigma^g_w(\cdot)\) denotes the generalized Weyl spectrum. Cited in 2 Documents MSC: 47A10 Spectrum, resolvent 47A55 Perturbation theory of linear operators Keywords:upper triangular operator matrices; generalized Weyl operator; generalized Weyl spectrum PDFBibTeX XMLCite \textit{G. Li} et al., Mediterr. J. Math. 12, No. 3, 1059--1067 (2015; Zbl 1321.47008) Full Text: DOI References: [1] Apostol C.: The reduced minimum modulus. Mich. Math. J. 32, 279-294 (1985) · Zbl 0613.47008 · doi:10.1307/mmj/1029003239 [2] Benhida C., Zerouali E.H., Zguitti H.: Spectra of upper triangular operator matrices. Proc. Am. Math. Soc. 133, 3013-3020 (2005) · Zbl 1067.47005 · doi:10.1090/S0002-9939-05-07812-3 [3] Conway, J.B.: A Course in Functional Analysis. Springer, New York (1990) · Zbl 0706.46003 [4] Djordjević D.S.: On generalized Weyl operators. Proc. Am. Math. Soc. 130, 81-84 (2001) · Zbl 0982.47015 · doi:10.1090/S0002-9939-01-06081-6 [5] Djordjević D.S.: Perturbation of spectra of operator matrices. J. Op. Theory 48, 467-486 (2002) · Zbl 1019.47003 [6] Du H., Pan J.: Perturbation of spectrums of 2 × 2 operator matrices. Proc. Am. Math. Soc. 121, 761-766 (1994) · Zbl 0814.47016 · doi:10.1090/S0002-9939-1994-1185266-2 [7] Hai, G., Chen, A.: Moore-Penrose spectrums of 2 × 2 upper triangular operator matrices. Sys. Sci. Math. 29 (2009), 962-970. (In Chinese) · Zbl 1210.47011 [8] Lee W.Y.: Weyl spectra of operator matrices. Proc. Am. Math. Soc. 129, 131-138 (2000) · Zbl 0965.47011 · doi:10.1090/S0002-9939-00-05846-9 [9] Zguitti H.: A note on Drazin invertibility for upper triangular block operators. Mediterr. J. Math. 10, 1497-1507 (2013) · Zbl 1304.47005 · doi:10.1007/s00009-013-0275-z This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.