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Abstract and Applied Analysis
Volume 2011, Article ID 540212, 9 pages
http://dx.doi.org/10.1155/2011/540212
Research Article

Partial Isometries and EP Elements in Banach Algebras

Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, P.O. Box 224, 18000 Niš, Serbia

Received 29 January 2011; Revised 1 April 2011; Accepted 6 April 2011

Academic Editor: Ljubisa Kocinac

Copyright © 2011 Dijana Mosić and Dragan S. Djordjević. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. V. Rakočević, “Moore-Penrose inverse in Banach algebras,” Proceedings of the Royal Irish Academy. Section A, vol. 88, no. 1, pp. 57–60, 1988. View at Google Scholar
  2. V. Rakočević, “On the continuity of the Moore-Penrose inverse in Banach algebras,” Facta Universitatis. Series: Mathematics and Informatics, no. 6, pp. 133–138, 1991. View at Google Scholar · View at Zentralblatt MATH
  3. P. Robert, “On the group-inverse of a linear transformation,” Journal of Mathematical Analysis and Applications, vol. 22, pp. 658–669, 1968. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. E. Boasso, “On the Moore-Penrose inverse, EP Banach space operators, and EP Banach algebra elements,” Journal of Mathematical Analysis and Applications, vol. 339, no. 2, pp. 1003–1014, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. I. Vidav, “Eine metrische Kennzeichnung der selbstadjungierten Operatoren,” Mathematische Zeitschrift, vol. 66, pp. 121–128, 1956. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. C. Schmoeger, “Generalized projections in Banach algebras,” Linear Algebra and Its Applications, vol. 430, no. 2-3, pp. 601–608, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. E. Boasso and V. Rakočević, “Characterizations of EP and normal Banach algebra elements,” Linear Algebra and Its Applications, vol. 435, pp. 342–353, 2011. View at Google Scholar
  8. O. M. Baksalary, G. P. H. Styan, and G. Trenkler, “On a matrix decomposition of Hartwig and Spindelböck,” Linear Algebra and Its Applications, vol. 430, no. 10, pp. 2798–2812, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. O. M. Baksalary and G. Trenkler, “Characterizations of EP, normal, and Hermitian matrices,” Linear and Multilinear Algebra, vol. 56, no. 3, pp. 299–304, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. S. Cheng and Y. Tian, “Two sets of new characterizations for normal and EP matrices,” Linear Algebra and Its Applications, vol. 375, pp. 181–195, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. D. S. Djordjević, “Products of EP operators on Hilbert spaces,” Proceedings of the American Mathematical Society, vol. 129, no. 6, pp. 1727–1731, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. D. S. Djordjević, “Characterizations of normal, hyponormal and EP operators,” Journal of Mathematical Analysis and Applications, vol. 329, no. 2, pp. 1181–1190, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. D. S. Djordjević and J. J. Koliha, “Characterizing Hermitian, normal and EP operators,” Filomat, vol. 21, no. 1, pp. 39–54, 2007. View at Publisher · View at Google Scholar
  14. D. S. Djordjević, J. J. Koliha, and I. Straškraba, “Factorization of EP elements in C-algebras,” Linear and Multilinear Algebra, vol. 57, no. 6, pp. 587–594, 2009. View at Publisher · View at Google Scholar
  15. D. Drivaliaris, S. Karanasios, and D. Pappas, “Factorizations of EP operators,” Linear Algebra and Its Applications, vol. 429, no. 7, pp. 1555–1567, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. R. E. Hartwig and I. J. Katz, “On products of EP matrices,” Linear Algebra and Its Applications, vol. 252, pp. 339–345, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. J. J. Koliha, “A simple proof of the product theorem for EP matrices,” Linear Algebra and Its Applications, vol. 294, no. 1–3, pp. 213–215, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. J. J. Koliha, “Elements of C-algebras commuting with their Moore-Penrose inverse,” Studia Mathematica, vol. 139, no. 1, pp. 81–90, 2000. View at Google Scholar
  19. G. Lešnjak, “Semigroups of EP linear transformations,” Linear Algebra and Its Applications, vol. 304, no. 1–3, pp. 109–118, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. D. Mosić, D. S. Djordjević, and J. J. Koliha, “EP elements in rings,” Linear Algebra and Its Applications, vol. 431, no. 5–7, pp. 527–535, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. D. Mosić and D. S. Djordjević, “Partial isometries and EP elements in rings with involution,” Electronic Journal of Linear Algebra, vol. 18, pp. 761–772, 2009. View at Google Scholar · View at Zentralblatt MATH
  22. D. Mosić and D. S. Djordjević, “EP elements in Banach algebras,” Banach Journal of Mathematical Analysis, vol. 5, no. 2, pp. 25–32, 2011. View at Google Scholar
  23. P. Patrício and R. Puystjens, “Drazin-Moore-Penrose invertibility in rings,” Linear Algebra and Its Applications, vol. 389, pp. 159–173, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 15, Springer, New York, NY, USA, 2nd edition, 2003.
  25. S. L. Campbell and C. D. Meyer Jr., “EP operators and generalized inverses,” Canadian Mathematical Bulletin, vol. 18, no. 3, pp. 327–333, 1975. View at Google Scholar · View at Zentralblatt MATH
  26. J. J. Koliha, D. Djordjević, and D. Cvetković, “Moore-Penrose inverse in rings with involution,” Linear Algebra and Its Applications, vol. 426, no. 2-3, pp. 371–381, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. D. S. Djordjević and V. Rakočević, Lectures on Generalized Inverses, Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia, 2008.
  28. R. Harte and M. Mbekhta, “On generalized inverses in C-algebras,” Studia Mathematica, vol. 103, no. 1, pp. 71–77, 1992. View at Google Scholar