Song, Guang-Jing Common solutions to some operator equations over Hilbert \(C^{\ast}\)-modules and applications. (English) Zbl 1315.47015 Linear Multilinear Algebra 62, No. 7, 895-912 (2014). The author presents some necessary and sufficient conditions for the existence of a solution to the system of equations \(A_1XB_1 = C_1\), \(A_2XB_2 = C_2\), \(A_3XB_3 = C_3\) for adjointable operators between Hilbert \(C^*\)-modules, and gives the general solution of this system of equations. Reviewer: Mohammad Sal Moslehian (Karlstad) Cited in 2 Documents MSC: 47A62 Equations involving linear operators, with operator unknowns 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.) 47B65 Positive linear operators and order-bounded operators 46L08 \(C^*\)-modules 15A09 Theory of matrix inversion and generalized inverses 15A24 Matrix equations and identities Keywords:Hilbert \(C^{\ast}\)-module; system of operator equations; Moore-Penrose inverse PDFBibTeX XMLCite \textit{G.-J. Song}, Linear Multilinear Algebra 62, No. 7, 895--912 (2014; Zbl 1315.47015) Full Text: DOI References: [1] Chen JL, Special matrices (2001) [2] DOI: 10.1016/j.cpc.2009.10.019 · Zbl 1205.81086 [3] DOI: 10.1137/0131050 · Zbl 0359.65033 [4] DOI: 10.1016/0024-3795(79)90102-2 · Zbl 0403.47005 [5] DOI: 10.1016/j.laa.2008.05.012 · Zbl 1149.47011 [6] DOI: 10.1016/j.laa.2008.01.030 · Zbl 1153.47012 [7] DOI: 10.1016/j.laa.2012.05.012 · Zbl 1276.47018 [8] DOI: 10.1016/j.laa.2010.05.023 · Zbl 1214.47015 [9] DOI: 10.7153/oam-05-24 · Zbl 1227.47007 [10] DOI: 10.1016/j.jmaa.2012.07.001 · Zbl 1264.47021 [11] DOI: 10.15352/bjma/1363784232 · Zbl 1263.15016 [12] DOI: 10.1016/j.laa.2008.05.034 · Zbl 1147.47014 [13] Dieudonné J. Quasihermitian operators, In: Proceedings of International Symposium on Linear Spaces; Jerusalem; 1961. p. 115–122. [14] DOI: 10.1016/j.laa.2010.04.001 · Zbl 1193.47028 [15] DOI: 10.1307/mmj/1029000220 · Zbl 0182.45904 [16] DOI: 10.1016/j.laa.2008.08.021 · Zbl 1162.47021 [17] DOI: 10.2307/2372552 · Zbl 0051.09101 [18] Wegge-Olsen NE, K-theory and C*-algebras-a friendly approach (1993) [19] DOI: 10.4064/sm210-2-6 · Zbl 1270.46053 [20] DOI: 10.1016/j.laa.2007.08.035 · Zbl 1142.47003 [21] DOI: 10.1016/j.laa.2009.01.003 · Zbl 1166.47003 [22] DOI: 10.1016/j.laa.2009.02.010 · Zbl 1180.15019 [23] DOI: 10.1016/j.laa.2003.12.039 · Zbl 1058.15015 [24] DOI: 10.1007/s11425-010-4154-9 · Zbl 1218.15008 [25] DOI: 10.1016/S0024-3795(02)00345-2 · Zbl 1016.15003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.