# The reverse order law for EP modular operators

Volume 16, Issue 3, pp 412-418
Publication Date: September 15, 2016 Submission Date: January 10, 2016
• 2069 Views

### Authors

Javad Farokhi-ostad - Department of Basic Sciences, Birjand University of Technology, Birjand, Iran. Mehdi Mohammadzadeh Karizaki - University of Torbat Heydarieh, Torbat Heydariyeh, Iran.

### Abstract

In this paper, we present new conditions that reverse order law holds for EP modular operators.

### Share and Cite

##### ISRP Style

Javad Farokhi-ostad, Mehdi Mohammadzadeh Karizaki, The reverse order law for EP modular operators, Journal of Mathematics and Computer Science, 16 (2016), no. 3, 412-418

##### Chicago/Turabian Style

Farokhi-ostad, Javad, Karizaki, Mehdi Mohammadzadeh. "The reverse order law for EP modular operators." Journal of Mathematics and Computer Science, 16, no. 3 (2016): 412-418

### Keywords

• EP operator
• reverse order law
• Moore-Penrose inverse
• Hilbert $C^*$-module
• closed range.

•  47A05
•  46L08
•  15A09

### References

• [1] T. Aghasizadeh, S. Hejazian , Maps preserving semi-Fredholm operators on Hilbert $C^*$-modules, J. Math. Anal. Appl., 354 (2009), 625-629.

• [2] R. Bouldin , The product of operators with closed range , Tôhoku Math. J., 25 (1973), 359-363.

• [3] R. Bouldin , Closed range and relative regularity for products , J. Math. Anal. Appl., 61 (1977), 397-403.

• [4] D. S. Djordjević , Products of EP operators on Hilbert spaces , Proc. Amer. Math. Soc., 129 (2001), 1727-1731.

• [5] D. S. Djordjević, Further results on the reverse order law for generalized inverses, SIAM J. Matrix Anal. Appl., 29 (2007), 1242-1246.

• [6] M. Frank , Self-duality and $C^*$-reflexivity of Hilbert $C^*$-moduli , Z. Anal. Anwendungen, 9 (1990), 165-176.

• [7] M. Frank , Geometrical aspects of Hilbert $C^*$-modules, Positivity, 3 (1999), 215-243.

• [8] T. N. E. Greville , Note on the generalized inverse of a matrix product, SIAM Rev., 8 (1966), 518-521.

• [9] S. Izumino , The product of operators with closed range and an extension of the reverse order law, Tôhoku Math. J., 34 (1982), 43-52.

• [10] E. C. Lance, Hilbert $C^*$-modules, A toolkit for operator algebraists, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge (1995)

• [11] M. Mohammadzadeh Karizaki, M. Hassani, M. Amyari , Moore-Penrose inverse of product operators in Hilbert $C^*$-modules, Filomat, 30 (2016), 3397-3402

• [12] M. Mohammadzadeh Karizaki, M. Hassani, M. Amyari, M. Khosravi, Operator matrix of Moore-Penrose inverse operators on Hilbert $C^*$-modules , Colloq. Math., 140 (2015), 171-182

• [13] K. Sharifi , The product of operators with closed range in Hilbert $C^*$-modules , Linear Algebra Appl., 435 (2011), 1122-1130.

• [14] K. Sharifi , EP modular operators and their products, J. Math. Anal. Appl., 419 (2014), 870-877.

• [15] K. Sharifi, B. A. Bonakdar, The reverse order law for Moore-Penrose inverses of operators on Hilbert $C^*$-modules, Bull. Iranian Math. Soc., 42 (2016), 53-60.

• [16] Q. Xu, L. Sheng, Positive semi-definite matrices of adjointable operators on Hilbert $C^*$-modules, Linear Algebra Appl., 428 (2008), 992-1000.