On left and right west-stampfli decomposition
DOI:
https://doi.org/10.5269/bspm.47975Abstract
In this paper we deï¬ne and investigate the decomposition of a Hilbert space operator T in the form T = K+Q where K is a compact and the approximate points spectrum (or the surjectivity spectrum) of Q is identical to the set of all accumulation point of the approximate point spectrum ( or the surjectivity spectrum) of T. Also, we provide the relation between operators having these decomposition and left (or right) Stampfli operators.
References
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3. P. Aiena, J E Sanabria, On left and right poles of the resolvent. Acta Sci. Math.(Szeged). 74, 669-687, (2008).
4. C. Bensalloua, M. Nadir, General note on the theorem of Stampfli, M. J Inequal Appl. 2016:55, (2016). https://doi.org/10.1186/s13660-016-1002-7
5. J. Conway, A Course in Functional Analysis, Graduate Texts in Mathematics, Springer, (1990).
6. B. P. Duggal, Isolated eigenvalues, poles and compact perturbations of Banach space operators, arXiv:1808.03542v2. (2018). https://doi.org/10.7153/oam-2019-13-67
7. B. P. Duggal, H. Kim, Generalized Browder, Weyl spectra and the polaroid property under compact perturbations, J. Korean Math. Soc. 54, 281-302, (2017). https://doi.org/10.4134/JKMS.j150728
8. R. E. Harte, Invertibility and singularity for bounded linear operators, Marcel Dekker, New york, (1988).
9. Herrero, D A, Approximation of Hilbert Space Operators, vol. 1, Research Notes in Mathematics, vol. 72. Pitman, London (1982).
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11. Mıcheal O Searcoid, A contribution to the solution of the compact correction problem for operators on a Banach space, Glasgow Math. J. 31, 219-229, (1989). https://doi.org/10.1017/S0017089500007771
12. J. G. Stampfli, Compact perturbations, normal eigenvalues and a problem of Salinas, J. London Math. Soc. (2) 9, 165-175, (1974). https://doi.org/10.1112/jlms/s2-9.1.165
13. V. Rakocevic, Approximate point spectrum and commuting compact perturbations, Glasgow Math.J. 28, 193-198, (1986). https://doi.org/10.1017/S0017089500006509
14. T. J. Laffey and T. T. West, Fredholm commutators, Proc. Roy. Irish Acad. Sect. A, 82, 129-140, (1982).
15. S. Zhu, C. G. Li, SVEP and compact perturbations, J. Math. Anal. Appl. 380, 69-75, (2011). https://doi.org/10.1016/j.jmaa.2011.02.036
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2022-01-24
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