On left and right west-stampfli decomposition
Abstract
In this paper we define 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.
Downloads
References
P. Aiena, Fredholm and local spectral theory II with application to Weyl-type theorems. Springer, (2018). https://doi.org/10.1007/978-3-030-02266-2
P. Aiena, E. Aponte, E. Bazan, Weyl type theorems for left and right polaroid operators, Int. Equa. Oper. Theory. 66, 1-20, (2010). https://doi.org/10.1007/s00020-009-1738-2
P. Aiena, J E Sanabria, On left and right poles of the resolvent. Acta Sci. Math.(Szeged). 74, 669-687, (2008).
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
J. Conway, A Course in Functional Analysis, Graduate Texts in Mathematics, Springer, (1990).
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
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
R. E. Harte, Invertibility and singularity for bounded linear operators, Marcel Dekker, New york, (1988).
Herrero, D A, Approximation of Hilbert Space Operators, vol. 1, Research Notes in Mathematics, vol. 72. Pitman, London (1982).
J. J. Koliha, P. W. Poon , On West and Stampfli decomposition, Acta Sci.Math. (Szeged). 63, 181-194, (1997).
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
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
V. Rakocevic, Approximate point spectrum and commuting compact perturbations, Glasgow Math.J. 28, 193-198, (1986). https://doi.org/10.1017/S0017089500006509
T. J. Laffey and T. T. West, Fredholm commutators, Proc. Roy. Irish Acad. Sect. A, 82, 129-140, (1982).
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
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
