Volume 67 | Issue 8 | Year 2021 | Article Id. IJMTT-V67I8P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I8P506
In this paper we investigated some equivalent condition of the reverse order law for the Core inverse in C*-algebra extending some well-known results to more general settings.
[1] O. M. Baksalary and G. Trenkler, Core inverse of matrices, Linear Multilinear Algebra 58 (2010), No. 6, 681 - 697.
[2] R. H. Bouldin, The Pseudo-inverse of a product, SIAM J. Appl. Math. 25, (1973), 489-495.
[3] R. H. Bouldin, Generalized inverses and factorization, recent applicition of generalized inverses, Pitman Ser. Res. Notes. Math. No. 66, (1982), 233 - 248.
[4] D. S. Djordjevic, Futher results on the reverse order law for the generalized inverses, SIAM J. Matrix Anal. Appl. 29, (4), (2007), 1242 - 1246.
[5] D. S. Djordjevic, Nebojsa, C. Dincic, Reverse order law for the Moore-Penrose inverses, J. Math. Anal. Appl. 361, (1), (2010), 252 - 261.
[6] D. S. Djordjevic, V. Rakocevic, \Lectures on Generalized Inverses, Facutly of Sciences and Mathe- matics, University of Nis, 2008.
[7] T. N. E. Greville, \Note on the generalized inverse of a matrix product, SIAM Rev. 8, (1966), 518-521.
[8] R. E. Harte, M. Mbekhta, \On generalized inverses in C-algebra, Studia Math. 103, (1992), 71-77.
[9] R. E. Hartwig, \The reverse law revisited, Linear Algebra Appl. 76, (1986), 241-246.
[10] S. Izumino, \The product of operator with closed range and an extensiom of the reverse order law, Tohoku Math. J. 34, (1982), 43 - 52.
[11] J. J. Koliha, D. S. Djordievic, D. Cvetkovic Ilic, \Moore-Penrose inverse in rings with involution, Linear Algebra Appl. 426, (2007), 371 - 381.
[12] J. J. Koliha, V. Rakocevic, \Range projections and the Moore-Penrose inverse in rings with invo- lution, Linear Multilinear Algebra 55, (2007), 103 - 112.
[13] D. Mosic, D. S. Djordievic, \Moore-Penrose invertible normal and Hermitian elements in rings, Linear Algebra Appl. 431, (5-7), (2009), 732-745. REFERENCES 11
[14] R. Penrose, \A generalized inverse of matrices, Proc. Cambridge Philos. Soc. 51, (1955), 406-413.
[15] D. S. Rakic, Nebojsa C. Dincic, D. S. Djordjevic, \Core inverse and core partial order of Hilbert space operators, Appl. Math. Comput. 244, (2014), 283 - 302.
[16] D. S. Rakic, Nebojsa C. Dincic, D. S. Djordjevic, \Group, Moore-Penrose, core and dual core inverse in rings with involution, Linear Algebra Appl. 463, (2014), 115 - 133.
[17] Y. Tian, \Using rank formulas to characterize equalities for Moore-Penrose inverses of matrix products, Appl. Math. Comput. 147, (2004), 581-600.
[18] Y. Tian, \The equivalence between (AB)y = ByAy and other mixed-type reverse order laws, Int. J. Math. Edu. Sci. Technol. 37, (3), (2006), 331 - 339.
[19] H. J. Werner, \When id B-A- is a generalized inverse of AB, Linear Algebra Appl. 210, (1994), 255-263.
D. Krishnaswamy, V. Vijayaselvi, "Further results on the reverse order law for the Core inverse in C ∗ -algebras," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 8, pp. 50-60, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I8P506