DENG Chun-Yuan . ON THE INVERTIBILITY OF HILBERT SPACE IDEMPOTENTS[J]. Acta mathematica scientia, Series B, 2014 , 34(2) : 523 -536 . DOI: 10.1016/S0252-9602(14)60025-4

[1] Baksalary J K, Baksalary O M. Nonsingularity of linear combinations of idempotent matrices. Linear Algebra Appl, 2004, 388: 25–29

[2] Ben´?tez J, Thome N. Idempotency of linear combinations of an idempotent matrix and a t-potent matrix that commute. Linear Algebra Appl, 2005, 403: 414–418

[3] Bu C J, Li M, Zhang K, et al. Group inverse for the block matrices with an invertible subblock. Appl Math Comput, 2009, 215: 132–139

[4] Buckholtz D. Inverting the difference of Hilbert space projections. Amer Math Monthly, 1997, 104: 60–61

[5] Campbell S L, Meyer C D. Generalized inverses of linear transformations. Dover Publication, 1991

[6] Choi M D, Wu P Y. Convex combinations of projections. Linear Algebra Appl, 1990, 136: 25–42

[7] Coll C, Thome N. Oblique projectors and group involutory matrices. Appl Math Comput, 2003, 140: 517–522

[8] Deng C Y. Characterizations and Representations of the Group Inverse Involving Idempotents. Linear Algebra Appl, 2011, 434: 1067–1079

[9] Du H K, Yao X Y, Deng C Y. Invertibility of linear combinations of two idempotents. Proc Amer Math Soc, 2005, 134: 1451–1457

[10] Fang L, Ji G X, Pang Y F. Maps preserving the idempotency of products of operators. Linear Algebra Appl, 2007, 426: 40–52

[11] Groß J. Nonsingularity ofthe difference of two oblique projectors. SIAM J Matrix Anal Appl, 1999, 21(2): 390–395

[12] Koliha J J, Rakoˇcevi´c V. Stability theorems for linear combinations of idempotents. Integr Equat Operat Theor, 2007, 58: 597–601

[13] Koliha J J, Rakoˇcevi´c V, Straˇskraba I. The difference and sum of projectors. Linear Algebra Appl, 2004, 388: 279–288

[14] Koliha J J, Rakocevic V. Invertibility of the sum of idempotents. Linear Algebra Appl, 2002, 50: 285–292

[15] Liu X J, Wu L L, Yu Y M. The group inverse of the combinations of two idempotent matrices. Linear Multilinear Algebra, 2011, 59: 101–115

[16] Liu X J, Hu C M. Expressions and Iterative Methods for the Weighted Group Inverses of Linear Operators on Banach Space. J Comput Appl Math, 2012, 14: 724–732

[17] Liu X F, Yang H. Further results on the group inverses and Drazin inverses of anti-triangular block matrices. Appl Math Comput, 2012, 218: 8978–8986

[18] Searle S R. Linear Models. New York: Wiley, 1971

[19] Wei Y M. On the perturbation of the group inverse and oblique projection. Appl Math Comput, 1999, 98: 29–42

[20] Zhang S F, Wu J D. The Drazin inverse of the linear combinations of two idempotents in the Banach algebra. Linear Algebra Appl, 2012, 436: 3132–3138

[21] Zuo K Z. Nonsingularity of the difference and the sum of two idempotent matrices. Linear Algebra Appl, 2010, 433: 476–482