Idempotent decomposition of regularity and characterization for the accumulation of associated spectrum

References

[1] P. Aiena, Fredholm and Local Spectral Theory II, Lecture Notes in Math. 2235, Springer, Cham, 2018. 10.1007/978-3-030-02266-2Search in Google Scholar

[2] R. Benjamin, Spectral mapping theorems for the upper Weyl and upper Browder spectra, Quaest. Math. 41 (2018), no. 7, 951–961. 10.2989/16073606.2017.1417924Search in Google Scholar

[3] R. Benjamin, N. J. Laustsen and S. Mouton, r-Fredholm theory in Banach algebras, Glasg. Math. J. 61 (2019), no. 3, 615–627. 10.1017/S0017089518000393Search in Google Scholar

[4] M. Berkani, Continuous Fredholm theory, regularities and semiregularities, Complex Anal. Oper. Theory 15 (2021), no. 6, Paper No. 105. 10.1007/s11785-021-01151-1Search in Google Scholar

[5] M. Berkani and J. J. Koliha, Weyl type theorems for bounded linear operators, Acta Sci. Math. (Szeged) 69 (2003), no. 1–2, 359–376. Search in Google Scholar

[6] E. Boasso, Drazin spectra of Banach space operators and Banach algebra elements, J. Math. Anal. Appl. 359 (2009), no. 1, 48–55. 10.1016/j.jmaa.2009.05.036Search in Google Scholar

[7] X. Cao, M. Guo and B. Meng, Weyl spectra and Weyl’s theorem, J. Math. Anal. Appl. 288 (2003), no. 2, 758–767. 10.1016/j.jmaa.2003.09.026Search in Google Scholar

[8] X. Cao, H. Zhang and Y. Zhang, Consistent invertibility and Weyl’s theorem, J. Math. Anal. Appl. 369 (2010), no. 1, 258–264. 10.1016/j.jmaa.2010.03.023Search in Google Scholar

[9] J. Dong and X. H. Cao, The (generalized) Weylness of upper triangular operator matrices, Anal. Math. 46 (2020), no. 3, 465–481. 10.1007/s10476-020-0035-9Search in Google Scholar

[10] W. B. Gong and D. G. Han, Spectrum of the products of operators and compact perturbations, Proc. Amer. Math. Soc. 120 (1994), no. 3, 755–760. 10.1090/S0002-9939-1994-1197538-6Search in Google Scholar

[11] J. J. Grobler, H. Raubenheimer and A. Swartz, The index for Fredholm elements in a Banach algebra via a trace II, Czechoslovak Math. J. 66(141) (2016), no. 1, 205–211. 10.1007/s10587-016-0250-5Search in Google Scholar

[12] Y. Hadder and A. El Amrani, Characterizations of a commutative semisimple modular annihilator Banach algebra through its socle, Proyecciones 40 (2021), no. 3, 697–709. 10.22199/issn.0717-6279-4459Search in Google Scholar

[13] Y. Hadder, A. El Amrani and A. Blali, On the generalized Fredholm spectrum in a complex semisimple banach algebra, Rend. Circ. Mat. Palermo (2) 72 (2023), no. 1, 65–70. 10.1007/s12215-021-00651-5Search in Google Scholar

[14] R. Harte, Fredholm theory relative to a Banach algebra homomorphism, Math. Z. 179 (1982), no. 3, 431–436. 10.1007/BF01215344Search in Google Scholar

[15] S. Ivković, On compressions and generalized spectra of operators over C * -algebras, Ann. Funct. Anal. 11 (2020), no. 3, 505–522. 10.1007/s43034-019-00034-zSearch in Google Scholar

[16] S. Ivković, Semi-Fredholm theory in C * -algebras, Banach J. Math. Anal. 17 (2023), no. 3, Paper No. 51. 10.1007/s43037-023-00277-ySearch in Google Scholar

[17] Q. Jiang and H. Zhong, Generalized Kato decomposition, single-valued extension property and approximate point spectrum, J. Math. Anal. Appl. 356 (2009), no. 1, 322–327. 10.1016/j.jmaa.2009.03.017Search in Google Scholar

[18] D. J. Kečkić and Z. Lazović, Fredholm operators on C * -algebras, Acta Sci. Math. (Szeged) 83 (2017), no. 3–4, 629–655. 10.14232/actasm-015-526-5Search in Google Scholar

[19] J. J. Koliha, A generalized Drazin inverse, Glasg. Math. J. 38 (1996), no. 3, 367–381. 10.1017/S0017089500031803Search in Google Scholar

[20] J. J. Koliha, Isolated spectral points, Proc. Amer. Math. Soc. 124 (1996), no. 11, 3417–3424. 10.1090/S0002-9939-96-03449-1Search in Google Scholar

[21] Y. Y. Kong, L. N. Jiang and Y. X. Ren, The Weyl’s theorem and its perturbations in semisimple Banach algebra, Acta Math. Sin. (Engl. Ser.) 37 (2021), no. 5, 675–688. 10.1007/s10114-021-0434-2Search in Google Scholar

[22] V. Kordula and V. Müller, On the axiomatic theory of spectrum, Studia Math. 119 (1996), no. 2, 109–128. 10.4064/sm-119-2-129-147Search in Google Scholar

[23] N. J. Laustsen, Matrix multiplication and composition of operators on the direct sum of an infinite sequence of Banach spaces, Math. Proc. Cambridge Philos. Soc. 131 (2001), no. 1, 165–183. 10.1017/S0305004101005138Search in Google Scholar

[24] S. Mouton, Generalized spectral perturbation and the boundary spectrum, Czechoslovak Math. J. 71(146) (2021), no. 2, 603–621. 10.21136/CMJ.2021.0046-20Search in Google Scholar

[25] V. Müller, Axiomatic theory of spectrum. III. Semiregularities, Studia Math. 142 (2000), no. 2, 159–169. 10.4064/sm-142-2-159-169Search in Google Scholar

[26] V. Müller, Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras, Oper. Theory Adv. Appl. 139, Birkhäuser, Basel, 2007. Search in Google Scholar

[27] H. Raubenheimer and A. Swartz, Radius preserving (semi)regularities in Banach algebras, Quaest. Math. 42 (2019), no. 6, 811–822. 10.2989/16073606.2018.1501439Search in Google Scholar

[28] Y. Ren and L. Jiang, Left and right-Drazin inverses in rings and operator algebras, J. Algebra Appl. 23 (2024), no. 4, Article ID 2450064. 10.1142/S0219498824500646Search in Google Scholar

[29] S. Č. Živković-Zlatanović and M. Berkani, Topological uniform descent, quasi-Fredholmness and operators originated from semi-B-Fredholm theory, Complex Anal. Oper. Theory 13 (2019), no. 8, 3595–3622. 10.1007/s11785-019-00920-3Search in Google Scholar

[30] S. Č. Živković-Zlatanović and M. D. Cvetković, Generalized Kato–Riesz decomposition and generalized Drazin–Riesz invertible operators, Linear Multilinear Algebra 65 (2017), no. 6, 1171–1193. 10.1080/03081087.2016.1231771Search in Google Scholar