Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE GENERALIZED INVERSES A(1,2)T,S OF THE ADJOINTABLE OPERATORS ON THE HILBERT C^*-MODULES

  • Xu, Qingxiang (Department of Mathematics, Shanghai Normal University) ;
  • Zhang, Xiaobo (Department of Mathematics, Shanghai Normal University)
  • Published : 2010.03.01
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Abstract

In this paper, we introduce and study the generalized inverse $A^{(1,2)}_{T,S}$ with the prescribed range T and null space S of an adjointable operator A from one Hilbert $C^*$-module to another, and get some analogous results known for finite matrices over the complex field or associated rings, and the Hilbert space operators.

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References

  1. D. S. Djordjevic and P. S. Stanimirovic, On the generalized Drazin inverse and generalized resolvent, Czechoslovak Math. J. 51(126) (2001), no. 3, 617–634. https://doi.org/10.1023/A:1013792207970
  2. D. S. Djordjevi´c and Y. Wei, Outer generalized inverses in rings, Comm. Algebra 33 (2005), no. 9, 3051–3060. https://doi.org/10.1081/AGB-200066112
  3. J. J. Koliha, A generalized Drazin inverse, Glasgow Math. J. 38 (1996), no. 3, 367–381. https://doi.org/10.1017/S0017089500031803
  4. E. C. Lance, Hilbert C*-modules, A toolkit for operator algebraists. London Mathematical Society Lecture Note Series, 210. Cambridge University Press, Cambridge, 1995.
  5. G. K. Pedersen, $C{\ast}$-algebras and their automorphism groups, London Mathematical Society Monographs, 14. Academic Press, Inc., London-New York, 1979.
  6. G. Wang, Y. Wei, and S. Qiao, Generalized Inverses: theory and computations, Science Press, Beijing-New York, 2004.
  7. Y. Wei, A characterization and representation of the generalized inverse $A^{(2)}_{T,S}$ and its applications, Linear Algebra Appl. 280 (1998), no. 2-3, 87–96. https://doi.org/10.1016/S0024-3795(98)00008-1
  8. Q. Xu and L. Sheng, Positive semi-definite matrices of adjointable operators on Hilbert $C{\ast}$-modules, Linear Algebra Appl. 428 (2008), no. 4, 992–1000. https://doi.org/10.1016/j.laa.2007.08.035
  9. Y. Yu and G. Wang, The generalized inverse $A^{(2)}_{T,S}$ of a matrix over an associative ring, J. Aust. Math. Soc. 83 (2007), no. 3, 423–437. https://doi.org/10.1017/S1446788700038015
  10. B. Zheng and C. Zhong, Existence and expressions for the generalized inverse $A^{(2)}_{T,S}$ of linear operators on Hilbert spaces, Acta Math. Sci. Ser. A Chin. Ed. 27 (2007), no. 2, 288–295.

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