On the Normality of the Product of Tow Operators in Hilbert Space

Main Article Content

Benali Abdelkader, Mohammed Meziane, Mohammed Hichem Mortad


In this paper we present the results of the maximality of operators not nec-essarily bounded. For that, we will see the results obtained by operators in situation ofextension. Regarding the normal product of normal operators we seem to be the key tomaximality.

Article Details


  1. J. B. Conway, A course in functional analysis, (2nd edition), Springer, 1990 .
  2. A. Devinatz, A. E. Nussbaum, J. von Neumann, On the Permutability of Self-adjoint Operators, Ann. Math. 62 (2) (1955), 199-203.
  3. A. Devinatz, A. E. Nussbaum, On the Permutability of Normal Operators, Ann. Math. 65 (2) (1957), 144-152.
  4. B. Abdelkader and H. Mortad Mohammed, Generalizations of Kaplansky ´s Theorem Involving Unbounded Linear Operators. Bull. Polish Acad. Sci. Math. 62 (2) (2014), 181-186.
  5. K. Gustafson, M. H. Mortad, Unbounded Products of Operators and Connections to Dirac-Type Operators, Bull. Sci. Math., 138 (5) (2014), 626-642.
  6. K. Gustafson, M. H. Mortad, Conditions Implying Commutativity of Unbounded Self-adjoint Operators and Related Topics, J. Oper. Theory, 76 (1) (2016), 159-169.
  7. Il Bong Jung, M. H. Mortad, J. Stochel, On normal products of selfadjoint operators, Kyungpook Math. J. 57 (2017), 457-471.
  8. M. H. Mortad, An All-Unbounded-Operator Version of the Fuglede-Putnam Theorem, Complex Anal. Oper. Theory, 6 (6) (2012), 1269-1273.
  9. M. H. Mortad, Commutativity of Unbounded Normal and Self-adjoint Operators and Applications, Oper. Matrices, 8 (2) (2014), 563-571.
  10. M.H. Mortad, A criterion for the normality of unbounded operators and applications to self-adjointness, Rend. Circ. Mat. Palermo, 64 (2015), 149-156.
  11. M. Meziane, M.H. Mortad, Maximality of linear operators, Rend. Circ. Mat. Palmero, Ser. 2, 68 (2019), 441-451
  12. C. Chellali, M.H. Mortad, Commutativity up to a factor of bounded operators and applications, J. Math. Anal. Appl. 419 (2014), 114-122.
  13. A. E. Nussbaum, A Commutativity Theorem for Unbounded Operators in Hilbert Space, Trans. Amer. Math. Soc. 140 (1969), 485-491.
  14. F. C. Paliogiannis, A generalization of the Fuglede-Putnam theorem to unbounded operators, J. Oper. 2015 (2015). Art. ID 804353.
  15. W. Rudin, Functional Analysis, McGraw-Hill Book Co., Second edition, International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991.
  16. K. Schm ¨udgen, Unbounded Self-adjoint Operators on Hilbert Space, Springer GTM 265 (2012).
  17. Z. Sebesty ´en, J. Stochel, On suboperators with codimension one domains, J. Math. Anal. Appl. 360 (2009), 391-397.
  18. J. Stochel, An asymmetric Putnam-Fuglede theorem for unbounded operators, Proc. Amer. Math. Soc. 129 (2001), 2261- 2271.
  19. J. Stochel, F. H. Szafraniec, Domination of unbounded operators and commutativity, J. Math. Soc. Japan, 55 (2003), 405-437.
  20. J. Weidmann, Linear operators in Hilbert spaces (translated from the German by J. Sz ¨ucs), Srpinger-Verlag, GTM 68 (1980).