Positive and real-positive solutions to the equation axa*=c in C*-algebras

Linear and Multilinear Algebra

Volumn 55, Issue 6, 2007, Pages 535-543

  Cvetkovic Ilic, D ^a   Dajic, Alegra ^b   Koliha, J J ^b  

^a UNIVERSITY OF NI   (Serbia)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

C* algebra; Equation in a C* algebra; Hilbert space; Matrix equation; Moore Penrose inverse; Operator equation; Positive solution; Real positive solution; Regular element

Indexed keywords

EID: 35148857933     PISSN: 03081087     EISSN: 15635139     Source Type: Journal    
DOI: 10.1080/03081080701248112     Document Type: Article

References (13)

1. Albert, A., 1969, Conditions for positive and nonnegative definiteness in terms of pseudoinverses. SIAM Journal on Applied Mathematics, 17, 434-440.
2. Baksalary, J.K., 1984, Nonnegative definite and positive definite solutions to the matrix equation AXA* = B. Linear and Multilinear Algebra, 16, 133-139.
3. Cvetković-Ilić, D.S., Djordjevió, D.S. and Rakočević, V., 2005, Schur complements in C*-algebras. Mathematische Nachrichten, 278, 808-814.
4. Groß, J., 1998, A note on the general Hermitian solution to AXA* = B. Bulletin of the Malaysian Mathematical Society (2), 21, 57-62.
5. Groß, J., 2000, Nonnegative definite and positive definite solutions to the matrix equation AXA* = B-revisited. Linear Algebra and its Applications, 321, 123-129.
6. Harte, R.E. and Mbekhta, M., 1992, On generalized inverses in C*-algebras. Studia Mathematica, 103, 71-77.
7. Khatri, C.G. and Mitra, S.K., 1976, Hermitian and nonnegative definite solutions of linear matrix equations. SIAM Journal on Applied Mathematics, 31, 579-585.
8. Penrose, R., 1955, A generalized inverse for matrices. Proceedings of the Cambridge Philosophical Society, 51, 406-413.
9. Zhang, Xian, 2004, The general common Hermitian nonnegative-definite solution to the matrix equations AXA* = B and CXC* = D. Linear and Multilinear Algebra, 52, 49-60.
10. Zhang, Xian, 2005, The general common Hermitian nonnegative-definite solution to the matrix equations AXA* = BB* and CXC* = DD* with applications in statistics. Journal of Multivariate Analysis, 93, 257-266.
11. Zhang, Xian and Cheng, Mei-Yu, 2003, The rank-constrained Hermitian nonnegative-definite and positive-definite solutions to the matrix equation AXA* = B. Linear Algebra and its Applications, 370, 163-174.
12. Zhang, Xian and Cheng, Mei-Yu, 2004, The general common nonnegative-definite and positive-definite solutions to the matrix equations AXA* = BB* and CXC* = DD*. Applied Mathematics Letters, 17, 543-547.
13. T = C in the symmetric and skew-antisymmetric matrix set (Chinese). Journal of Mathematical Research and Exposition, 25, 292-298.