Quotient operators: new generation of linear operators

Gherbi Abdellah, Messirdi Bekkai, Benharrat Mohammed


In this paper we attempt to investigate some algebraic and topological properties of quotient operators acting on Hilbert space, and to give a characterization of Fredholm quotient operator and its index.

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A. Ben-Israel and T.N.E. Greville, Generalized Inverses: Theory and Applications.

Second edition, Springer, New York, 2003.

Bruce, A. Barnes, Majorization, range inclusion, and factorisation

for bounded linear operators, Proc. Amer. Math. Soc, 2005, 133, 155-162

H. O. Cordes and J. P. Labrousse, The invariance of the index in the metric space of closed operators. J Math. Mech. 12 (1963), 693-719.

G. Djellouli, S. Messirdi and B. Messirdi, Some Stronger Topologies for Closed Operators in Hilbert Space.Int. J. Contemp. Math. Sciences, 2010, 5, no. 25, 1223 - 1232.

D. S. Djordjevic, Characterizations of normal, hyponormal and EP operators. J. Math. Anal. Appl. 2007, 329, 1181-1190.

R. G. Douglas, On majorization and range inclusion of operators in Hilbert space, Proc. Amer. Math. Soc. 1966, 17, 413-416.

P.A. Fillmore, J.P. Williams, On operator ranges, Adv. Math. 1971, 7, 254-281.

S. Goldberg, Unbounded Linear Operators. McGraw-Hill, New-York, 1966.

G. Hirasawa, Quotient of bounded operators and Kaufman's theorem. Math. J. Toyama Univ. 1995, 18, 215-224.

S. Izumino, Quotients of bounded operators, Proc. Amer. Math. Soc. 1989, 106, 427-435.

S. Izumino, Quotients of bounded operators and their weak adjoints, J. Operator theory. 1993, 29,83-96

T. Kato, Perturbation theory for linear operators,

Springer-Verlag, New York, 1966.

W. E. Kaufman, Representing a closed operator as a quotient of continuous operators, Proc.

Amer. Math. Soc. 1978, 72, 531-534.

W. E. Kaufman, Semiclosed operators in Hilbert space, Proc. Amer. Math. Soc. 1979, 76, 67-73.

W. E. Kaufman, Closed operators and pure contractions in Hilbert space, Proc. Amer. Math. Soc. 1983, 87, 83-87.

J-Ph. Labrousse, Inverses généralisés d'opérateurs non bornés , Proc. Amer. Math. Soc. 1992, 115, 125-129.

J. S. Mac-Nerney, Investigation concerning positive definite continued fractions. Duke Math.J. 1959, 26,663-678.

Amer. Math. Soc. 1978, 72, 531-534.

S. Messirdi, M. Djaa and B. Messirdi, Stability of Almost Closed Operators on a Hilbert Space. Sarajevo J. of Math. 2009, 5(17), 133-141.


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