The reverse order law for EP modular operators
-
2673
Downloads
-
4215
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
AMA Style
Farokhi-ostad Javad, Karizaki Mehdi Mohammadzadeh, The reverse order law for EP modular operators. J Math Comput SCI-JM. (2016); 16(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.
MSC
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.