The core inverses of differences and products of projections in rings with involution
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas - Tập 113 - Trang 3283-3296 - 2019
Tóm tắt
Let R be a unital ring with involution. The core inverses of differences and products of projections in R are investigated. Let $$p, q\in R$$ be two projections, we obtained equivalent conditions such that $$p-q$$, $$(p-q)^2$$, $$1-qp$$, $$pq+qp$$ and $$(pq-qp)^2$$ are core invertible, respectively. Moreover, expressions for their core inverses are given.
Tài liệu tham khảo
Baksalary, O.M., Trenkler, G.: Core inverse of matrices. Linear Multilinear Algebra 58, 681–697 (2010)
Ma, HF., Li, TT.: Characterizations and representations of the core inverse and its applications. Linear Multilinear Algebra. https://doi.org/10.1080/03081087.2019.1588847
Rakić, D.S., Dinčić, N.Č., Djordiević, D.S.: Group, Moore–Penrose, core and dual core inverse in rings with involution. Linear Algebra Appl 463, 115–133 (2014)
Xu, S.Z., Chen, J.L., Zhang, X.X.: New characterizations for core and dual core inverses in rings with involution. Front. Math. China. 12(1), 231–246 (2017)
Du, H.K., Deng, C.Y.: Moore–Penrose inverses of products and differences of orthogonal projections. Acta Anal. Funct. Appl. 8, 104–109 (2006)
Li, Y.: The Moore–Penrose inverses of products and differences of projections in a \(C^{\ast }\)-algebra. Linear Algebra Appl 428, 1169–1177 (2008)
Deng, C.Y., Wei, Y.M.: Further results on the Moore–Penrose invertibility of projectors and its applications. Linear Multilinear Algebra 60, 109–129 (2012)
Zhang, X.X., Zhang, S.S., Chen, J.L., Wang, L.: Moore–Penrose invertibility of differences and products of projections in rings with involution. Linear Algebra Appl 439, 4101–4109 (2013)
Chen, J.L., Zhu, H.H.: Drazin invertibility of product and difference of idempotents in a ring. Filomat 28(6), 1133–1137 (2014)
Benítez, J., Cvetković-Ilić, D.: Equalities of ideals associated with two projections in rings with involution. Linear Multilinear Algebra 61(10), 1419–1435 (2013)
Hartwig, R.E.: Block generalized inverses. Arch. Retional Mech. Anal. 61, 197–251 (1976)
Xu, S. Z., Chen, J. L., Benítez, J.: EP elements in rings with involution. Bull. Malays. Math. Sci. Soc. https://doi.org/10.1007/s40840-019-00731-x
Chen, J.L., Zhu, H.H., Patrício, P., Zhang, Y.L.: Characterizations and representations of core and dual core inverses. Can. Math. Bull. 60(2), 269–282 (2017)
Penrose, R.: A generalized inverse for matrices. Proc. Camb. Philos. Soc. 51, 406–413 (1955)
Mosić, D., Deng, C.Y., Ma, H.F.: On a weighted core inverse in a ring with involution. Commun. Algebra 46(6), 2332–2345 (2018)
Mosić, D.: One-sided core partial orders on a ring with involution. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Ser. A. Matemáticas 112(4), 1367–1379 (2018)