Title: On the Normality of the Product of Tow Operators in Hilbert Space
Author(s): Benali Abdelkader, Mohammed Meziane, Mohammed Hichem Mortad
Pages: 624-632
Cite as:
Benali Abdelkader, Mohammed Meziane, Mohammed Hichem Mortad, On the Normality of the Product of Tow Operators in Hilbert Space, Int. J. Anal. Appl., 18 (4) (2020), 624-632.


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.

Full Text: PDF



  1. J. B. Conway, A course in functional analysis, (2nd edition), Springer, 1990 . Google Scholar

  2. A. Devinatz, A. E. Nussbaum, J. von Neumann, On the Permutability of Self-adjoint Operators, Ann. Math. 62 (2) (1955), 199-203. Google Scholar

  3. A. Devinatz, A. E. Nussbaum, On the Permutability of Normal Operators, Ann. Math. 65 (2) (1957), 144-152. Google Scholar

  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. Google Scholar

  5. K. Gustafson, M. H. Mortad, Unbounded Products of Operators and Connections to Dirac-Type Operators, Bull. Sci. Math., 138 (5) (2014), 626-642. Google Scholar

  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. Google Scholar

  7. Il Bong Jung, M. H. Mortad, J. Stochel, On normal products of selfadjoint operators, Kyungpook Math. J. 57 (2017), 457-471. Google Scholar

  8. M. H. Mortad, An All-Unbounded-Operator Version of the Fuglede-Putnam Theorem, Complex Anal. Oper. Theory, 6 (6) (2012), 1269-1273. Google Scholar

  9. M. H. Mortad, Commutativity of Unbounded Normal and Self-adjoint Operators and Applications, Oper. Matrices, 8 (2) (2014), 563-571. Google Scholar

  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. Google Scholar

  11. M. Meziane, M.H. Mortad, Maximality of linear operators, Rend. Circ. Mat. Palmero, Ser. 2, 68 (2019), 441–451 Google Scholar

  12. C. Chellali, M.H. Mortad, Commutativity up to a factor of bounded operators and applications, J. Math. Anal. Appl. 419 (2014), 114-122. Google Scholar

  13. A. E. Nussbaum, A Commutativity Theorem for Unbounded Operators in Hilbert Space, Trans. Amer. Math. Soc. 140 (1969), 485-491. Google Scholar

  14. F. C. Paliogiannis, A generalization of the Fuglede-Putnam theorem to unbounded operators, J. Oper. 2015 (2015). Art. ID 804353. Google Scholar

  15. W. Rudin, Functional Analysis, McGraw-Hill Book Co., Second edition, International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991. Google Scholar

  16. K. Schm¨udgen, Unbounded Self-adjoint Operators on Hilbert Space, Springer GTM 265 (2012). Google Scholar

  17. Z. Sebesty´en, J. Stochel, On suboperators with codimension one domains, J. Math. Anal. Appl. 360 (2009), 391-397. Google Scholar

  18. J. Stochel, An asymmetric Putnam-Fuglede theorem for unbounded operators, Proc. Amer. Math. Soc. 129 (2001), 2261- 2271. Google Scholar

  19. J. Stochel, F. H. Szafraniec, Domination of unbounded operators and commutativity, J. Math. Soc. Japan, 55 (2003), 405-437. Google Scholar

  20. J. Weidmann, Linear operators in Hilbert spaces (translated from the German by J. Sz¨ucs), Srpinger-Verlag, GTM 68 (1980). Google Scholar


Copyright © 2020 IJAA, unless otherwise stated.