Acknowledgement
The second named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1F1A1057574).
References
- J. K. Baksalary and X. J. Liu, An alternative characterization of generalized projectors, Linear Algebra Appl. 388 (2004), 61-65. https://doi.org/10.1016/j.laa.2004.01.010
- B. A. Barnes, Common operator properties of the linear operators RS and SR, Proc. Amer. Math. Soc. 126 (1998), no. 4, 1055-1061. https://doi.org/10.1090/S0002-9939-98-04218-X
- A. Brown and C. M. Pearcy, Spectra of tensor products of operators, Proc. Amer. Math. Soc. 17 (1966), 162-166. https://doi.org/10.2307/2035080
- J. J. Buoni and J. D. Faires, Ascent, descent, nullity and defect of products of operators, Indiana Univ. Math. J. 25 (1976), no. 7, 703-707. https://doi.org/10.1512/iumj.1976.25.25054
- H. K. Du and Y. Li, The spectral characterization of generalized projections, Linear Algebra Appl. 400 (2005), 313-318. https://doi.org/10.1016/j.laa.2004.11.027
- B. P. Duggal and I. H. Kim, Products of generalized n-projections, Linear Multilinear Algebra. https://doi.org/10.1080/03081087.2021.2002249
- J. Gross and G. Trenkler, Generalized and hypergeneralized projectors, Linear Algebra Appl. 264 (1997), 463-474. https://doi.org/10.1016/S0024-3795(96)00541-1
- H. G. Heuser, Functional Analysis, translated from the German by John Horvath, A Wiley-Interscience Publication, John Wiley & Sons, Ltd., Chichester, 1982.
- L. Lebtahi and N. Thome, A note on k-generalized projections, Linear Algebra Appl. 420 (2007), no. 2-3, 572-575. https://doi.org/10.1016/j.laa.2006.08.011