Banach Journal of Mathematical Analysis

EP elements in Banach algebras

Dragan S. Djordjevic and Dijana Mosic

Full-text: Open access


An element of a Banach algebra is EP, if it commutes with its Moore-Penrose inverse. We present a number of new characterizations of EP elements in Banach algebra.

Article information

Banach J. Math. Anal., Volume 5, Number 2 (2011), 25-32.

First available in Project Euclid: 14 August 2011

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)

EP elements Moore-Penrose inverse group inverse Banach algebra


Mosic, Dijana; Djordjevic, Dragan S. EP elements in Banach algebras. Banach J. Math. Anal. 5 (2011), no. 2, 25--32. doi:10.15352/bjma/1313362999.

Export citation


  • O.M. Baksalary and G. Trenkler, Characterizations of EP, normal and Hermitian matrices, Linear Multilinear Algebra 56 (2006), 299–304.
  • A. Ben-Israel and T.N.E. Greville, Generalized Inverses: Theory and Applications, 2nd ed., Springer, New York, 2003.
  • E. Boasso, On the Moore–Penrose inverse, EP Banach space operators, and EP Banach algebra elements, J. Math. Anal. Appl. 339 (2008), 1003–1014.
  • E. Boasso and V. Rakočević, Characterizations of EP and normal Banach algebra elements, Linear Algebra Appl. (to appear).
  • S.L. Campbell and C.D. Meyer Jr., EP operators and generalized inverses, Canad. Math. Bull. 18 (1975), 327–333.
  • S. Cheng and Y. Tian, Two sets of new characterizations for normal and EP matrices, Linear Algebra Appl. 375 (2003), 181–195.
  • D.S. Djordjević, Products of EP operators on Hilbert spaces, Proc. Amer. Math. Soc. 129 (6) (2000), 1727-1731.
  • D.S. Djordjević, Characterization of normal, hyponormal and EP operators, J. Math. Anal. Appl. 329 (2) (2007), 1181-1190.
  • D.S. Djordjević and J.J. Koliha, Characterizing hermitian, normal and EP operators, Filomat 21:1 (2007), 39–54.
  • D.S. Djordjević, J.J. Koliha and I. Straškraba, Factorization of EP elements in $C^*$-algebras, Linear Multilinear Algebra 57 (6) (2009), 587–594.
  • D.S. Djordjević and V. Rakočević, Lectures on Generalized Inverses, Faculty of Sciences and Mathematics, University of Niš, 2008.
  • D. Drivaliaris, S. Karanasios and D. Pappas, Factorizations of EP operators, Liner Algebra Appl. 429 (7) (2008) 1555–1567.
  • R.E. Harte and M. Mbekhta, On generalized inverses in C*-algebras, Studia Math. 103 (1992), 71–77.
  • R.E. Hartwig and I.J. Katz, On products of EP matrices, Linear Algebra Appl. 252 (1997), 339-345.
  • J.J. Koliha, A simple proof of the product theorem for EP matrices, Linear Algebra Appl. 294 (1999), 213–215.
  • J.J. Koliha, Elements of C*-algebras commuting with their Moore–Penrose inverse, Studia Math. 139 (2000), 81–90.
  • G. Lesnjak, Semigroups of EP linear transformations, Linear Algebra Appl. 304 (1-3) (2000), 109–118.
  • M. Mbekhta, Partial isometries and generalized inverses, Acta Sci. Math. (Szeged) 70 (2004), 767–781.
  • D. Mosi\' c, D.S. Djordjević and J.J. Koliha, EP elements in rings, Linear Algebra Appl. 431 (2009), 527–535.
  • P. Patrí cio and R. Puystjens, Drazin–Moore–Penrose invertibility in rings, Linear Algebra Appl. 389 (2004), 159–173.
  • V. Rakočević, Moore-Penrose inverse in Banach algebras, Proc. R. Ir. Acad. Ser. A 88 (1) (1988), 57–60.
  • V. Rakočević, On the continuity of the Moore-Penrose inverse in Banach algebras, Facta Univ. Ser. Math. Inform. 6 (1991), 133–138.
  • P. Robert, On the group inverse of a linear transformation, J. Math. Anal. Appl. 22 (1968), 658–669.