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Linear and Multilinear Algebra Volume 55, 2007 - Issue 6
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Original Articles

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

D. Cvetković-Ilić Faculty of Mathematics and Sciences, University of Niš, Višegradska 33, 18000 Niš, Serbia
,
Alegra Dajić Department of Mathematics and Statistics, University of Melbourne, Melbourne, VIC 3010, Australia
&
J. J. Koliha Department of Mathematics and Statistics, University of Melbourne, Melbourne, VIC 3010, AustraliaCorrespondence[email protected]
Pages 535-543 | Received 07 Aug 2006, Accepted 23 Jan 2007, Published online: 09 Oct 2007

References

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  • Cvetković-Ilić , DS , Djordjević , DS and Rakočević , V . 2005 . Schur complements in C*-algebras . Mathematische Nachrichten , 278 : 808 – 814 .
  • Groß , J . 1998 . A note on the general Hermitian solution to AXA* = B . Bulletin of the Malaysian Mathematical Society (2) , 21 : 57 – 62 .
  • Groß , J . 2000 . Nonnegative definite and positive definite solutions to the matrix equation AXA*=B–revisited . Linear Algebra and its Applications , 321 : 123 – 129 .
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  • 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 .
  • 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 .
  • 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 .
  • Zhou , Fu-Zhao . 2005 . Solutions of the matrix equation AXAT = C in the symmetric and skew-antisymmetric matrix set (Chinese) . Journal of Mathematical Research and Exposition , 25 : 292 – 298 .

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