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Linear and Multilinear Algebra Volume 68, 2020 - Issue 10
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Articles

Conditions that the product of operators is an EP operator in Hilbert C*-module

Maryam Jalaeiana Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
,
Mehdi Mohammadzadeh Karizakib Department of Computer Engineering, University of Torbat Heydarieh, Torbat Heydarieh, IranCorrespondence[email protected]
&
Mahmoud Hassania Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
Pages 1990-2004 | Received 24 Jul 2018, Accepted 09 Dec 2018, Published online: 16 Jan 2019

References

  • Schwerdtfeger H. Introduction to linear algebra and the theory of matrices. Groningen: P. Noordhoff; 1950.
  • Harte R, Mbekhta M. On generalized inverses in C∗-algebras. Studia Math. 1992;103(1):71–77. doi: 10.4064/sm-103-1-71-77
  • Harte R, Mbekhta M. On generalized inverses in C∗-algebras II. Studia Math. 1993;106:129–138. doi: 10.4064/sm-106-2-129-138
  • Koliha JJ. The Drazin and Moore–Penrose inverse in C∗-algebras. Math Proc R Ir Acad. 1999;99A(1):17–27.
  • Koliha JJ. Elements of C∗-algebras commuting with their Moore–Penrose inverse. Studia Math. 2000;139(1):81–90. doi: 10.4064/sm-139-1-81-90
  • Hartwig RE. Block generalized inverses. Arch Rational Mech Anal. 1976;61(3):197–251. doi: 10.1007/BF00281485
  • Hartwig RE. Generalized inverses, EP elements and associates. Rev Roumaine Math Pures Appl. 1978;23(1):57–60.
  • Boasso E. On the Moore–Penrose inverse, EP Banach space operators, and EP Banach algebra elements. J Math Anal Appl. 2008;339(2):1003–1014. doi: 10.1016/j.jmaa.2007.07.059
  • Drivaliaris D, Karanasios S, Pappas D. Factorizations of EP operators. Liner Algebra Appl. 2008;429(7):1555–1567. doi: 10.1016/j.laa.2008.04.026
  • Hartwig RE, Katz IJ. On product of EP matrices. Linear Algebra Appl. 1997;252:339–345. doi: 10.1016/0024-3795(95)00693-1
  • Djordjević DS. Products of EP operators on Hilbert spaces. Proc Amer Math Soc. 2000;129(6):1727–1731. doi: 10.1090/S0002-9939-00-05701-4
  • Mohammadzadeh Karizaki M, Djordjević DS. Commuting C∗ modular operators. Aequationes Math. 2016;90(6):1103–1114. doi: 10.1007/s00010-016-0424-0
  • Hartwig RE, Spindelböck K. Matrices for which A∗ and A† can commute. Linear Multilinear Algebra. 1984;14:241–256. doi: 10.1080/03081088308817561
  • Lance EC. Hilbert C*-modules-a toolkit for operator algebraists. Cambridge: Cambridge University Press; 1995.
  • Mohammadzadeh Karizaki M, Hassani M, Amyari M. Moore–Penrose inverse of product operators in Hilbert C∗-modules. Filomat. 2016;30(13):3397–3402. doi: 10.2298/FIL1613397M
  • Xu Q, Sheng L. Positive semi-definite matrices of adjointable operators on Hilbert C∗-modules. Linear Algebra Appl. 2008;428(4):992–1000. doi: 10.1016/j.laa.2007.08.035
  • Mohammadzadeh Karizaki M, Hassani M, Amyari M, et al. Operator matrix of Moore–Penrose inverse operators on Hilbert C∗-modules. Colloq Math. 2015;140:171–182. doi: 10.4064/cm140-2-2
  • Sharifi K, Ahmadi Bonakdar B. the reverse order law for Moore–Penrose inverses of operators on Hilbert C∗-modules. B Iran Math Soc. 2016;42:53–60.
  • Katz IJ. Weigmann type theorems for EPr matrices. Duke Math J. 1965;32:423–428. doi: 10.1215/S0012-7094-65-03242-4
  • Djordjević DS. Further results on the reverse order law for generalized inverses. SIAM J Matrix Anal Appl. 2007;29(4):1242–1246. doi: 10.1137/050638114

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